From ecddec6e3b93c5f4f9d82b76edb89e082c83f343 Mon Sep 17 00:00:00 2001
From: xinoehp512 <38770806+xinoehp512@users.noreply.github.com>
Date: Mon, 29 May 2023 18:01:47 -0400
Subject: [PATCH] Fixed incorrectly formatted output & incorrectly formatted
 documentation for the following generators: (#424)

-Complex Quadratic
-Absolute Difference
-Stationary Points
-Volume of a Cube
-Quotient of Powers with Same Base
-Union, Intersection, Difference of Two Sets
-Probability of a certain sum appearing on faces of dice
---
 docs/mathgenerator.html                  |  38 +-
 docs/mathgenerator/_gen_list.html        |  15 +-
 docs/mathgenerator/_latexBuilder.html    |  16 +-
 docs/mathgenerator/algebra.html          | 241 ++++++----
 docs/mathgenerator/basic_math.html       | 116 +++--
 docs/mathgenerator/calculus.html         |  50 +-
 docs/mathgenerator/computer_science.html |  72 +--
 docs/mathgenerator/geometry.html         | 554 ++++++++++++-----------
 docs/mathgenerator/misc.html             | 162 +++----
 docs/mathgenerator/statistics.html       |  46 +-
 docs/search.js                           |   2 +-
 mathgenerator/algebra.py                 |  10 +-
 mathgenerator/basic_math.py              |   2 +-
 mathgenerator/calculus.py                |   4 +-
 mathgenerator/geometry.py                |   1 +
 mathgenerator/misc.py                    |  12 +-
 mathgenerator/statistics.py              |   2 +-
 17 files changed, 720 insertions(+), 623 deletions(-)
diff --git a/docs/mathgenerator.html b/docs/mathgenerator.html
index 520875b..b18934d 100644
--- a/docs/mathgenerator.html
+++ b/docs/mathgenerator.html
@@ -3,14 +3,14 @@
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+    <style>/*! layout.css */html, body{width:100%;height:100%;}html, main{scroll-behavior:smooth;}body{background-color:var(--pdoc-background);}@media (max-width:769px){#navtoggle{cursor:pointer;position:absolute;width:50px;height:40px;top:1rem;right:1rem;border-color:var(--text);color:var(--text);display:flex;opacity:0.8;z-index:999;}#navtoggle:hover{opacity:1;}#togglestate + div{display:none;}#togglestate:checked + div{display:inherit;}main, header{padding:2rem 3vw;}header + main{margin-top:-3rem;}.git-button{display:none !important;}nav input[type="search"]{max-width:77%;}nav input[type="search"]:first-child{margin-top:-6px;}nav input[type="search"]:valid ~ *{display:none !important;}}@media (min-width:770px){:root{--sidebar-width:clamp(12.5rem, 28vw, 22rem);}nav{position:fixed;overflow:auto;height:100vh;width:var(--sidebar-width);}main, header{padding:3rem 2rem 3rem calc(var(--sidebar-width) + 3rem);width:calc(54rem + var(--sidebar-width));max-width:100%;}header + main{margin-top:-4rem;}#navtoggle{display:none;}}#togglestate{position:absolute;height:0;opacity:0;}nav.pdoc{--pad:clamp(0.5rem, 2vw, 1.75rem);--indent:1.5rem;background-color:var(--accent);border-right:1px solid var(--accent2);box-shadow:0 0 20px rgba(50, 50, 50, .2) inset;padding:0 0 0 var(--pad);overflow-wrap:anywhere;scrollbar-width:thin; scrollbar-color:var(--accent2) transparent }nav.pdoc::-webkit-scrollbar{width:.4rem; }nav.pdoc::-webkit-scrollbar-thumb{background-color:var(--accent2); }nav.pdoc > div{padding:var(--pad) 0;}nav.pdoc .module-list-button{display:inline-flex;align-items:center;color:var(--text);border-color:var(--muted);margin-bottom:1rem;}nav.pdoc .module-list-button:hover{border-color:var(--text);}nav.pdoc input[type=search]{display:block;outline-offset:0;width:calc(100% - var(--pad));}nav.pdoc .logo{max-width:calc(100% - var(--pad));max-height:35vh;display:block;margin:0 auto 1rem;transform:translate(calc(-.5 * var(--pad)), 0);}nav.pdoc ul{list-style:none;padding-left:0;}nav.pdoc > div > ul{margin-left:calc(0px - var(--pad));}nav.pdoc li a{padding:.2rem 0 .2rem calc(var(--pad) + var(--indent));}nav.pdoc > div > ul > li > a{padding-left:var(--pad);}nav.pdoc li{transition:all 100ms;}nav.pdoc li:hover{background-color:var(--nav-hover);}nav.pdoc a, nav.pdoc a:hover{color:var(--text);}nav.pdoc a{display:block;}nav.pdoc > h2:first-of-type{margin-top:1.5rem;}nav.pdoc .class:before{content:"class ";color:var(--muted);}nav.pdoc .function:after{content:"()";color:var(--muted);}nav.pdoc footer:before{content:"";display:block;width:calc(100% - var(--pad));border-top:solid var(--accent2) 1px;margin-top:1.5rem;padding-top:.5rem;}nav.pdoc footer{font-size:small;}</style>
+    <style>/*! content.css */.pdoc{color:var(--text);box-sizing:border-box;line-height:1.5;background:none;}.pdoc .pdoc-button{cursor:pointer;display:inline-block;border:solid black 1px;border-radius:2px;font-size:.75rem;padding:calc(0.5em - 1px) 1em;transition:100ms all;}.pdoc .pdoc-alert{padding:1rem 1rem 1rem calc(1.5rem + 24px);border:1px solid transparent;border-radius:.25rem;background-repeat:no-repeat;background-position:1rem center;margin-bottom:1rem;}.pdoc .pdoc-alert > *:last-child{margin-bottom:0;}.pdoc .pdoc-alert-note {color:#084298;background-color:#cfe2ff;border-color:#b6d4fe;background-image:url("data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A//www.w3.org/2000/svg%22%20width%3D%2224%22%20height%3D%2224%22%20fill%3D%22%23084298%22%20viewBox%3D%220%200%2016%2016%22%3E%3Cpath%20d%3D%22M8%2016A8%208%200%201%200%208%200a8%208%200%200%200%200%2016zm.93-9.412-1%204.705c-.07.34.029.533.304.533.194%200%20.487-.07.686-.246l-.088.416c-.287.346-.92.598-1.465.598-.703%200-1.002-.422-.808-1.319l.738-3.468c.064-.293.006-.399-.287-.47l-.451-.081.082-.381%202.29-.287zM8%205.5a1%201%200%201%201%200-2%201%201%200%200%201%200%202z%22/%3E%3C/svg%3E");}.pdoc .pdoc-alert-warning{color:#664d03;background-color:#fff3cd;border-color:#ffecb5;background-image:url("data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A//www.w3.org/2000/svg%22%20width%3D%2224%22%20height%3D%2224%22%20fill%3D%22%23664d03%22%20viewBox%3D%220%200%2016%2016%22%3E%3Cpath%20d%3D%22M8.982%201.566a1.13%201.13%200%200%200-1.96%200L.165%2013.233c-.457.778.091%201.767.98%201.767h13.713c.889%200%201.438-.99.98-1.767L8.982%201.566zM8%205c.535%200%20.954.462.9.995l-.35%203.507a.552.552%200%200%201-1.1%200L7.1%205.995A.905.905%200%200%201%208%205zm.002%206a1%201%200%201%201%200%202%201%201%200%200%201%200-2z%22/%3E%3C/svg%3E");}.pdoc .pdoc-alert-danger{color:#842029;background-color:#f8d7da;border-color:#f5c2c7;background-image:url("data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A//www.w3.org/2000/svg%22%20width%3D%2224%22%20height%3D%2224%22%20fill%3D%22%23842029%22%20viewBox%3D%220%200%2016%2016%22%3E%3Cpath%20d%3D%22M5.52.359A.5.5%200%200%201%206%200h4a.5.5%200%200%201%20.474.658L8.694%206H12.5a.5.5%200%200%201%20.395.807l-7%209a.5.5%200%200%201-.873-.454L6.823%209.5H3.5a.5.5%200%200%201-.48-.641l2.5-8.5z%22/%3E%3C/svg%3E");}.pdoc .visually-hidden{position:absolute !important;width:1px !important;height:1px !important;padding:0 !important;margin:-1px !important;overflow:hidden !important;clip:rect(0, 0, 0, 0) !important;white-space:nowrap !important;border:0 !important;}.pdoc h1, .pdoc h2, .pdoc h3{font-weight:300;margin:.3em 0;padding:.2em 0;}.pdoc > section:not(.module-info) h1{font-size:1.5rem;font-weight:500;}.pdoc > section:not(.module-info) h2{font-size:1.4rem;font-weight:500;}.pdoc > section:not(.module-info) h3{font-size:1.3rem;font-weight:500;}.pdoc > section:not(.module-info) h4{font-size:1.2rem;}.pdoc > section:not(.module-info) h5{font-size:1.1rem;}.pdoc a{text-decoration:none;color:var(--link);}.pdoc a:hover{color:var(--link-hover);}.pdoc blockquote{margin-left:2rem;}.pdoc pre{border-top:1px solid var(--accent2);border-bottom:1px solid var(--accent2);margin-top:0;margin-bottom:1em;padding:.5rem 0 .5rem .5rem;overflow-x:auto;background-color:var(--code);}.pdoc code{color:var(--text);padding:.2em .4em;margin:0;font-size:85%;background-color:var(--code);border-radius:6px;}.pdoc a > code{color:inherit;}.pdoc pre > code{display:inline-block;font-size:inherit;background:none;border:none;padding:0;}.pdoc > section:not(.module-info){margin-bottom:1.5rem;}.pdoc .modulename{margin-top:0;font-weight:bold;}.pdoc .modulename a{color:var(--link);transition:100ms all;}.pdoc .git-button{float:right;border:solid var(--link) 1px;}.pdoc .git-button:hover{background-color:var(--link);color:var(--pdoc-background);}.view-source-toggle-state,.view-source-toggle-state ~ .pdoc-code{display:none;}.view-source-toggle-state:checked ~ .pdoc-code{display:block;}.view-source-button{display:inline-block;float:right;font-size:.75rem;line-height:1.5rem;color:var(--muted);padding:0 .4rem 0 1.3rem;cursor:pointer;text-indent:-2px;}.view-source-button > span{visibility:hidden;}.module-info .view-source-button{float:none;display:flex;justify-content:flex-end;margin:-1.2rem .4rem -.2rem 0;}.view-source-button::before{position:absolute;content:"View Source";display:list-item;list-style-type:disclosure-closed;}.view-source-toggle-state:checked ~ .attr .view-source-button::before,.view-source-toggle-state:checked ~ .view-source-button::before{list-style-type:disclosure-open;}.pdoc .docstring{margin-bottom:1.5rem;}.pdoc section:not(.module-info) .docstring{margin-left:clamp(0rem, 5vw - 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     <style>/*! custom.css */</style><script>
     window.MathJax = {
         tex: {
@@ -43,8 +43,8 @@
             <input type="search" placeholder="Search..." role="searchbox" aria-label="search"
                    pattern=".+" required>
 
-        <h2>Contents</h2>
-        <ul>
+            <h2>Contents</h2>
+            <ul>
   <li><a href="#mathgenerator">mathgenerator</a>
   <ul>
     <li><a href="#table-of-contents">Table of Contents</a></li>
@@ -55,19 +55,19 @@
 </ul>
 
 
-        <h2>Submodules</h2>
-        <ul>
-                <li><a href="mathgenerator/algebra.html">algebra</a></li>
-                <li><a href="mathgenerator/basic_math.html">basic_math</a></li>
-                <li><a href="mathgenerator/calculus.html">calculus</a></li>
-                <li><a href="mathgenerator/computer_science.html">computer_science</a></li>
-                <li><a href="mathgenerator/geometry.html">geometry</a></li>
-                <li><a href="mathgenerator/misc.html">misc</a></li>
-                <li><a href="mathgenerator/statistics.html">statistics</a></li>
-        </ul>
+            <h2>Submodules</h2>
+            <ul>
+                    <li><a href="mathgenerator/algebra.html">algebra</a></li>
+                    <li><a href="mathgenerator/basic_math.html">basic_math</a></li>
+                    <li><a href="mathgenerator/calculus.html">calculus</a></li>
+                    <li><a href="mathgenerator/computer_science.html">computer_science</a></li>
+                    <li><a href="mathgenerator/geometry.html">geometry</a></li>
+                    <li><a href="mathgenerator/misc.html">misc</a></li>
+                    <li><a href="mathgenerator/statistics.html">statistics</a></li>
+            </ul>
 
-        <h2>API Documentation</h2>
-            <ul class="memberlist">
+            <h2>API Documentation</h2>
+                <ul class="memberlist">
             <li>
                     <a class="function" href="#get_gen_list">get_gen_list</a>
             </li>
@@ -117,7 +117,7 @@ mathgenerator    </h1>
 <p>The project can be install via pip</p>
 
 <div class="pdoc-code codehilite">
-<pre><span></span><code>pip install mathgenerator
+<pre><span></span><code>pip<span class="w"> </span>install<span class="w"> </span>mathgenerator
 </code></pre>
 </div>
 
@@ -418,7 +418,7 @@ You can also use <code><a href="#getGenList">getGenList()</a></code> to return a
                         if (doc.annotation)
                             heading += `<span class="annotation">${doc.annotation}</span>`;
                         if (doc.default_value)
-                            heading += `<span class="default_value">${doc.default_value}</span>`;
+                            heading += `<span class="default_value"> = ${doc.default_value}</span>`;
                         break;
                     default:
                         heading = `<span class="name">${doc.fullname}</span>`;
diff --git a/docs/mathgenerator/_gen_list.html b/docs/mathgenerator/_gen_list.html
index 0fe40f6..3913067 100644
--- a/docs/mathgenerator/_gen_list.html
+++ b/docs/mathgenerator/_gen_list.html
@@ -3,14 +3,14 @@
 <head>
     <meta charset="utf-8">
     <meta name="viewport" content="width=device-width, initial-scale=1">
-    <meta name="generator" content="pdoc 12.3.0"/>
+    <meta name="generator" content="pdoc 13.1.1"/>
     <title>mathgenerator._gen_list API documentation</title>
 
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     <style>/*! custom.css */</style><script>
     window.MathJax = {
         tex: {
@@ -50,8 +50,8 @@
 
 
 
-        <h2>API Documentation</h2>
-            <ul class="memberlist">
+            <h2>API Documentation</h2>
+                <ul class="memberlist">
     </ul>
 
 
@@ -202,7 +202,8 @@
 </span><span id="L-127"><a href="#L-127"><span class="linenos">127</span></a>    <span class="p">(</span><span class="s2">&quot;complementary_and_supplementary_angle&quot;</span><span class="p">,</span> <span class="s2">&quot;geometry&quot;</span><span class="p">),</span>
 </span><span id="L-128"><a href="#L-128"><span class="linenos">128</span></a>    <span class="p">(</span><span class="s2">&quot;simplify_square_root&quot;</span><span class="p">,</span> <span class="s2">&quot;basic_math&quot;</span><span class="p">),</span>
 </span><span id="L-129"><a href="#L-129"><span class="linenos">129</span></a>    <span class="p">(</span><span class="s2">&quot;line_equation_from_2_points&quot;</span><span class="p">,</span> <span class="s2">&quot;algebra&quot;</span><span class="p">),</span>
-</span><span id="L-130"><a href="#L-130"><span class="linenos">130</span></a><span class="p">]</span>
+</span><span id="L-130"><a href="#L-130"><span class="linenos">130</span></a>    <span class="p">(</span><span class="s2">&quot;orthogonal_projection&quot;</span><span class="p">,</span> <span class="s2">&quot;algebra&quot;</span><span class="p">),</span>
+</span><span id="L-131"><a href="#L-131"><span class="linenos">131</span></a><span class="p">]</span>
 </span></pre></div>
 
 
@@ -327,7 +328,7 @@
                         if (doc.annotation)
                             heading += `<span class="annotation">${doc.annotation}</span>`;
                         if (doc.default_value)
-                            heading += `<span class="default_value">${doc.default_value}</span>`;
+                            heading += `<span class="default_value"> = ${doc.default_value}</span>`;
                         break;
                     default:
                         heading = `<span class="name">${doc.fullname}</span>`;
diff --git a/docs/mathgenerator/_latexBuilder.html b/docs/mathgenerator/_latexBuilder.html
index 18d0f48..ad8aa97 100644
--- a/docs/mathgenerator/_latexBuilder.html
+++ b/docs/mathgenerator/_latexBuilder.html
@@ -3,14 +3,14 @@
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+    <meta name="generator" content="pdoc 13.1.1"/>
     <title>mathgenerator._latexBuilder API documentation</title>
 
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     <style>/*! custom.css */</style><script>
     window.MathJax = {
         tex: {
@@ -50,8 +50,8 @@
 
 
 
-        <h2>API Documentation</h2>
-            <ul class="memberlist">
+            <h2>API Documentation</h2>
+                <ul class="memberlist">
             <li>
                     <a class="function" href="#frac">frac</a>
             </li>
@@ -87,7 +87,7 @@
 </span><span id="L-3"><a href="#L-3"><span class="linenos"> 3</span></a>
 </span><span id="L-4"><a href="#L-4"><span class="linenos"> 4</span></a>
 </span><span id="L-5"><a href="#L-5"><span class="linenos"> 5</span></a><span class="k">def</span> <span class="nf">bmatrix</span><span class="p">(</span><span class="n">lst</span><span class="p">):</span>
-</span><span id="L-6"><a href="#L-6"><span class="linenos"> 6</span></a>    <span class="sd">&quot;&quot;&quot;Turns 2d matrix into a bmatrix&quot;&quot;&quot;</span>
+</span><span id="L-6"><a href="#L-6"><span class="linenos"> 6</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Turns 2d matrix into a bmatrix&quot;&quot;&quot;</span>
 </span><span id="L-7"><a href="#L-7"><span class="linenos"> 7</span></a>    <span class="n">out</span> <span class="o">=</span> <span class="sa">r</span><span class="s1">&#39;\begin</span><span class="si">{bmatrix}</span><span class="s1"> &#39;</span>
 </span><span id="L-8"><a href="#L-8"><span class="linenos"> 8</span></a>    <span class="n">lst</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39; &amp; &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="n">row</span><span class="p">))</span> <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">lst</span><span class="p">]</span>
 </span><span id="L-9"><a href="#L-9"><span class="linenos"> 9</span></a>    <span class="n">out</span> <span class="o">+=</span> <span class="sa">r</span><span class="s1">&#39; </span><span class="se">\\</span><span class="s1">\ &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">lst</span><span class="p">)</span>
@@ -131,7 +131,7 @@
     </div>
     <a class="headerlink" href="#bmatrix"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="bmatrix-6"><a href="#bmatrix-6"><span class="linenos"> 6</span></a><span class="k">def</span> <span class="nf">bmatrix</span><span class="p">(</span><span class="n">lst</span><span class="p">):</span>
-</span><span id="bmatrix-7"><a href="#bmatrix-7"><span class="linenos"> 7</span></a>    <span class="sd">&quot;&quot;&quot;Turns 2d matrix into a bmatrix&quot;&quot;&quot;</span>
+</span><span id="bmatrix-7"><a href="#bmatrix-7"><span class="linenos"> 7</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Turns 2d matrix into a bmatrix&quot;&quot;&quot;</span>
 </span><span id="bmatrix-8"><a href="#bmatrix-8"><span class="linenos"> 8</span></a>    <span class="n">out</span> <span class="o">=</span> <span class="sa">r</span><span class="s1">&#39;\begin</span><span class="si">{bmatrix}</span><span class="s1"> &#39;</span>
 </span><span id="bmatrix-9"><a href="#bmatrix-9"><span class="linenos"> 9</span></a>    <span class="n">lst</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39; &amp; &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="n">row</span><span class="p">))</span> <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">lst</span><span class="p">]</span>
 </span><span id="bmatrix-10"><a href="#bmatrix-10"><span class="linenos">10</span></a>    <span class="n">out</span> <span class="o">+=</span> <span class="sa">r</span><span class="s1">&#39; </span><span class="se">\\</span><span class="s1">\ &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">lst</span><span class="p">)</span>
@@ -283,7 +283,7 @@
                         if (doc.annotation)
                             heading += `<span class="annotation">${doc.annotation}</span>`;
                         if (doc.default_value)
-                            heading += `<span class="default_value">${doc.default_value}</span>`;
+                            heading += `<span class="default_value"> = ${doc.default_value}</span>`;
                         break;
                     default:
                         heading = `<span class="name">${doc.fullname}</span>`;
diff --git a/docs/mathgenerator/algebra.html b/docs/mathgenerator/algebra.html
index 4a14ddd..75e59ee 100644
--- a/docs/mathgenerator/algebra.html
+++ b/docs/mathgenerator/algebra.html
@@ -3,14 +3,14 @@
 <head>
     <meta charset="utf-8">
     <meta name="viewport" content="width=device-width, initial-scale=1">
-    <meta name="generator" content="pdoc 12.3.0"/>
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     <title>mathgenerator.algebra API documentation</title>
 
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@@ -50,8 +50,8 @@
 
 
 
-        <h2>API Documentation</h2>
-            <ul class="memberlist">
+            <h2>API Documentation</h2>
+                <ul class="memberlist">
             <li>
                     <a class="function" href="#basic_algebra">basic_algebra</a>
             </li>
@@ -118,6 +118,9 @@
             <li>
                     <a class="function" href="#vector_dot">vector_dot</a>
             </li>
+            <li>
+                    <a class="function" href="#orthogonal_projection">orthogonal_projection</a>
+            </li>
     </ul>
 
 
@@ -147,7 +150,7 @@
 </span><span id="L-6"><a href="#L-6"><span class="linenos">  6</span></a>
 </span><span id="L-7"><a href="#L-7"><span class="linenos">  7</span></a>
 </span><span id="L-8"><a href="#L-8"><span class="linenos">  8</span></a><span class="k">def</span> <span class="nf">basic_algebra</span><span class="p">(</span><span class="n">max_variable</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-9"><a href="#L-9"><span class="linenos">  9</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Basic Algebra</span>
+</span><span id="L-9"><a href="#L-9"><span class="linenos">  9</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Basic Algebra</span>
 </span><span id="L-10"><a href="#L-10"><span class="linenos"> 10</span></a>
 </span><span id="L-11"><a href="#L-11"><span class="linenos"> 11</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-12"><a href="#L-12"><span class="linenos"> 12</span></a><span class="sd">    | --- | --- |</span>
@@ -164,12 +167,12 @@
 </span><span id="L-23"><a href="#L-23"><span class="linenos"> 23</span></a>        <span class="k">return</span> <span class="n">x</span>
 </span><span id="L-24"><a href="#L-24"><span class="linenos"> 24</span></a>
 </span><span id="L-25"><a href="#L-25"><span class="linenos"> 25</span></a>    <span class="n">i</span> <span class="o">=</span> <span class="n">calculate_gcd</span><span class="p">((</span><span class="n">c</span> <span class="o">-</span> <span class="n">b</span><span class="p">),</span> <span class="n">a</span><span class="p">)</span>
-</span><span id="L-26"><a href="#L-26"><span class="linenos"> 26</span></a>    <span class="n">x</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="p">(</span><span class="n">c</span> <span class="o">-</span> <span class="n">b</span><span class="p">)</span><span class="o">//</span><span class="n">i</span><span class="si">}</span><span class="s2">/</span><span class="si">{</span><span class="n">a</span><span class="o">//</span><span class="n">i</span><span class="si">}</span><span class="s2">&quot;</span>
+</span><span id="L-26"><a href="#L-26"><span class="linenos"> 26</span></a>    <span class="n">x</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="p">(</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">b</span><span class="p">)</span><span class="o">//</span><span class="n">i</span><span class="si">}</span><span class="s2">/</span><span class="si">{</span><span class="n">a</span><span class="o">//</span><span class="n">i</span><span class="si">}</span><span class="s2">&quot;</span>
 </span><span id="L-27"><a href="#L-27"><span class="linenos"> 27</span></a>
 </span><span id="L-28"><a href="#L-28"><span class="linenos"> 28</span></a>    <span class="k">if</span> <span class="p">(</span><span class="n">c</span> <span class="o">-</span> <span class="n">b</span> <span class="o">==</span> <span class="mi">0</span><span class="p">):</span>
 </span><span id="L-29"><a href="#L-29"><span class="linenos"> 29</span></a>        <span class="n">x</span> <span class="o">=</span> <span class="s2">&quot;0&quot;</span>
 </span><span id="L-30"><a href="#L-30"><span class="linenos"> 30</span></a>    <span class="k">elif</span> <span class="n">a</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">a</span> <span class="o">==</span> <span class="n">i</span><span class="p">:</span>
-</span><span id="L-31"><a href="#L-31"><span class="linenos"> 31</span></a>        <span class="n">x</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">c</span> <span class="o">-</span> <span class="n">b</span><span class="si">}</span><span class="s2">&quot;</span>
+</span><span id="L-31"><a href="#L-31"><span class="linenos"> 31</span></a>        <span class="n">x</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">b</span><span class="si">}</span><span class="s2">&quot;</span>
 </span><span id="L-32"><a href="#L-32"><span class="linenos"> 32</span></a>
 </span><span id="L-33"><a href="#L-33"><span class="linenos"> 33</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="s2">x + </span><span class="si">{</span><span class="n">b</span><span class="si">}</span><span class="s2"> = </span><span class="si">{</span><span class="n">c</span><span class="si">}</span><span class="s2">$&quot;</span>
 </span><span id="L-34"><a href="#L-34"><span class="linenos"> 34</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">x</span><span class="si">}</span><span class="s2">$&quot;</span>
@@ -177,7 +180,7 @@
 </span><span id="L-36"><a href="#L-36"><span class="linenos"> 36</span></a>
 </span><span id="L-37"><a href="#L-37"><span class="linenos"> 37</span></a>
 </span><span id="L-38"><a href="#L-38"><span class="linenos"> 38</span></a><span class="k">def</span> <span class="nf">combine_like_terms</span><span class="p">(</span><span class="n">max_coef</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">max_exp</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_terms</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-39"><a href="#L-39"><span class="linenos"> 39</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Combine Like Terms</span>
+</span><span id="L-39"><a href="#L-39"><span class="linenos"> 39</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Combine Like Terms</span>
 </span><span id="L-40"><a href="#L-40"><span class="linenos"> 40</span></a>
 </span><span id="L-41"><a href="#L-41"><span class="linenos"> 41</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-42"><a href="#L-42"><span class="linenos"> 42</span></a><span class="sd">    | --- | --- |</span>
@@ -202,11 +205,11 @@
 </span><span id="L-61"><a href="#L-61"><span class="linenos"> 61</span></a>
 </span><span id="L-62"><a href="#L-62"><span class="linenos"> 62</span></a>
 </span><span id="L-63"><a href="#L-63"><span class="linenos"> 63</span></a><span class="k">def</span> <span class="nf">complex_quadratic</span><span class="p">(</span><span class="n">prob_type</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_range</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-64"><a href="#L-64"><span class="linenos"> 64</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Complex Quadratic Equation</span>
+</span><span id="L-64"><a href="#L-64"><span class="linenos"> 64</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Complex Quadratic Equation</span>
 </span><span id="L-65"><a href="#L-65"><span class="linenos"> 65</span></a>
 </span><span id="L-66"><a href="#L-66"><span class="linenos"> 66</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-67"><a href="#L-67"><span class="linenos"> 67</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="L-68"><a href="#L-68"><span class="linenos"> 68</span></a><span class="sd">    | Find the roots of given Quadratic Equation $x^2 + 8x + 8 = 0$ | $((-1.172, -6.828)) = (\frac{-8 + \sqrt{32}}{2*1}, (\frac{-8 - \sqrt{32}}{2*1})$ |</span>
+</span><span id="L-68"><a href="#L-68"><span class="linenos"> 68</span></a><span class="sd">    | Find the roots of given Quadratic Equation $x^2 + 8x + 8 = 0$ | $((-1.172, -6.828)) = (\frac{-8 + \sqrt{32}}{2}, (\frac{-8 - \sqrt{32}}{2})$ |</span>
 </span><span id="L-69"><a href="#L-69"><span class="linenos"> 69</span></a><span class="sd">    &quot;&quot;&quot;</span>
 </span><span id="L-70"><a href="#L-70"><span class="linenos"> 70</span></a>    <span class="k">if</span> <span class="n">prob_type</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">prob_type</span> <span class="o">&gt;</span> <span class="mi">1</span><span class="p">:</span>
 </span><span id="L-71"><a href="#L-71"><span class="linenos"> 71</span></a>        <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;prob_type not supported&quot;</span><span class="p">)</span>
@@ -251,9 +254,9 @@
 </span><span id="L-110"><a href="#L-110"><span class="linenos">110</span></a>
 </span><span id="L-111"><a href="#L-111"><span class="linenos">111</span></a>        <span class="k">if</span> <span class="n">sqrt_d</span> <span class="o">-</span> <span class="nb">int</span><span class="p">(</span><span class="n">sqrt_d</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
 </span><span id="L-112"><a href="#L-112"><span class="linenos">112</span></a>            <span class="n">sqrt_d</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">sqrt_d</span><span class="p">)</span>
-</span><span id="L-113"><a href="#L-113"><span class="linenos">113</span></a>            <span class="n">solution</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;(\frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> + </span><span class="si">{</span><span class="n">sqrt_d</span><span class="si">}</span><span class="s1">i</span><span class="se">}}{{</span><span class="s1">2*</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">, \frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> - </span><span class="si">{</span><span class="n">sqrt_d</span><span class="si">}</span><span class="s1">i</span><span class="se">}}{{</span><span class="s1">2*</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">)&#39;</span>
+</span><span id="L-113"><a href="#L-113"><span class="linenos">113</span></a>            <span class="n">solution</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;(\frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> + </span><span class="si">{</span><span class="n">sqrt_d</span><span class="si">}</span><span class="s1">i</span><span class="se">}}{{</span><span class="si">{</span><span class="mi">2</span><span class="o">*</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">, \frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> - </span><span class="si">{</span><span class="n">sqrt_d</span><span class="si">}</span><span class="s1">i</span><span class="se">}}{{</span><span class="si">{</span><span class="mi">2</span><span class="o">*</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">)&#39;</span>
 </span><span id="L-114"><a href="#L-114"><span class="linenos">114</span></a>        <span class="k">else</span><span class="p">:</span>
-</span><span id="L-115"><a href="#L-115"><span class="linenos">115</span></a>            <span class="n">solution</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;(\frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> + \sqrt</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">d</span><span class="si">}</span><span class="se">}}</span><span class="s1">i</span><span class="se">}}{{</span><span class="s1">2*</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">, \frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> - \sqrt</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">d</span><span class="si">}</span><span class="se">}}</span><span class="s1">i</span><span class="se">}}{{</span><span class="s1">2*</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">)&#39;</span>
+</span><span id="L-115"><a href="#L-115"><span class="linenos">115</span></a>            <span class="n">solution</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;(\frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> + \sqrt</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">d</span><span class="si">}</span><span class="se">}}</span><span class="s1">i</span><span class="se">}}{{</span><span class="si">{</span><span class="mi">2</span><span class="o">*</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">, \frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> - \sqrt</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">d</span><span class="si">}</span><span class="se">}}</span><span class="s1">i</span><span class="se">}}{{</span><span class="si">{</span><span class="mi">2</span><span class="o">*</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">)&#39;</span>
 </span><span id="L-116"><a href="#L-116"><span class="linenos">116</span></a>
 </span><span id="L-117"><a href="#L-117"><span class="linenos">117</span></a>        <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span><span id="L-118"><a href="#L-118"><span class="linenos">118</span></a>
@@ -265,11 +268,11 @@
 </span><span id="L-124"><a href="#L-124"><span class="linenos">124</span></a>
 </span><span id="L-125"><a href="#L-125"><span class="linenos">125</span></a>        <span class="k">if</span> <span class="n">sqrt_d</span> <span class="o">-</span> <span class="nb">int</span><span class="p">(</span><span class="n">sqrt_d</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
 </span><span id="L-126"><a href="#L-126"><span class="linenos">126</span></a>            <span class="n">sqrt_d</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">sqrt_d</span><span class="p">)</span>
-</span><span id="L-127"><a href="#L-127"><span class="linenos">127</span></a>            <span class="n">g_sol</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;(\frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> + </span><span class="si">{</span><span class="n">sqrt_d</span><span class="si">}</span><span class="se">}}{{</span><span class="s1">2*</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">, \frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> - </span><span class="si">{</span><span class="n">sqrt_d</span><span class="si">}</span><span class="se">}}{{</span><span class="s1">2*</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">)&#39;</span>
+</span><span id="L-127"><a href="#L-127"><span class="linenos">127</span></a>            <span class="n">g_sol</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;(\frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> + </span><span class="si">{</span><span class="n">sqrt_d</span><span class="si">}</span><span class="se">}}{{</span><span class="si">{</span><span class="mi">2</span><span class="o">*</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">, \frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> - </span><span class="si">{</span><span class="n">sqrt_d</span><span class="si">}</span><span class="se">}}{{</span><span class="si">{</span><span class="mi">2</span><span class="o">*</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">)&#39;</span>
 </span><span id="L-128"><a href="#L-128"><span class="linenos">128</span></a>        <span class="k">else</span><span class="p">:</span>
-</span><span id="L-129"><a href="#L-129"><span class="linenos">129</span></a>            <span class="n">g_sol</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;(\frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> + \sqrt</span><span class="se">{{</span><span class="si">{</span><span class="n">d</span><span class="si">}</span><span class="se">}}}}{{</span><span class="s1">2*</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">, (\frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> - \sqrt</span><span class="se">{{</span><span class="si">{</span><span class="n">d</span><span class="si">}</span><span class="se">}}}}{{</span><span class="s1">2*</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">)&#39;</span>
+</span><span id="L-129"><a href="#L-129"><span class="linenos">129</span></a>            <span class="n">g_sol</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;(\frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> + \sqrt</span><span class="se">{{</span><span class="si">{</span><span class="n">d</span><span class="si">}</span><span class="se">}}}}{{</span><span class="si">{</span><span class="mi">2</span><span class="o">*</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">, (\frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> - \sqrt</span><span class="se">{{</span><span class="si">{</span><span class="n">d</span><span class="si">}</span><span class="se">}}}}{{</span><span class="si">{</span><span class="mi">2</span><span class="o">*</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">)&#39;</span>
 </span><span id="L-130"><a href="#L-130"><span class="linenos">130</span></a>
-</span><span id="L-131"><a href="#L-131"><span class="linenos">131</span></a>        <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$(</span><span class="si">{</span><span class="n">s_root1</span><span class="p">,</span> <span class="n">s_root2</span><span class="si">}</span><span class="s1">) = </span><span class="si">{</span><span class="n">g_sol</span><span class="si">}</span><span class="s1">$&#39;</span>
+</span><span id="L-131"><a href="#L-131"><span class="linenos">131</span></a>        <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$(</span><span class="si">{</span><span class="n">s_root1</span><span class="p">,</span><span class="w"> </span><span class="n">s_root2</span><span class="si">}</span><span class="s1">) = </span><span class="si">{</span><span class="n">g_sol</span><span class="si">}</span><span class="s1">$&#39;</span>
 </span><span id="L-132"><a href="#L-132"><span class="linenos">132</span></a>
 </span><span id="L-133"><a href="#L-133"><span class="linenos">133</span></a>        <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span><span id="L-134"><a href="#L-134"><span class="linenos">134</span></a>
@@ -277,7 +280,7 @@
 </span><span id="L-136"><a href="#L-136"><span class="linenos">136</span></a><span class="k">def</span> <span class="nf">compound_interest</span><span class="p">(</span><span class="n">max_principle</span><span class="o">=</span><span class="mi">10000</span><span class="p">,</span>
 </span><span id="L-137"><a href="#L-137"><span class="linenos">137</span></a>                      <span class="n">max_rate</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
 </span><span id="L-138"><a href="#L-138"><span class="linenos">138</span></a>                      <span class="n">max_time</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-139"><a href="#L-139"><span class="linenos">139</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Compound Interest</span>
+</span><span id="L-139"><a href="#L-139"><span class="linenos">139</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Compound Interest</span>
 </span><span id="L-140"><a href="#L-140"><span class="linenos">140</span></a>
 </span><span id="L-141"><a href="#L-141"><span class="linenos">141</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-142"><a href="#L-142"><span class="linenos">142</span></a><span class="sd">    | --- | --- |</span>
@@ -293,7 +296,7 @@
 </span><span id="L-152"><a href="#L-152"><span class="linenos">152</span></a>
 </span><span id="L-153"><a href="#L-153"><span class="linenos">153</span></a>
 </span><span id="L-154"><a href="#L-154"><span class="linenos">154</span></a><span class="k">def</span> <span class="nf">distance_two_points</span><span class="p">(</span><span class="n">max_val_xy</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">min_val_xy</span><span class="o">=-</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="L-155"><a href="#L-155"><span class="linenos">155</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Distance between 2 points</span>
+</span><span id="L-155"><a href="#L-155"><span class="linenos">155</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Distance between 2 points</span>
 </span><span id="L-156"><a href="#L-156"><span class="linenos">156</span></a>
 </span><span id="L-157"><a href="#L-157"><span class="linenos">157</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-158"><a href="#L-158"><span class="linenos">158</span></a><span class="sd">    | --- | --- |</span>
@@ -315,7 +318,7 @@
 </span><span id="L-174"><a href="#L-174"><span class="linenos">174</span></a>              <span class="n">range_x2</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
 </span><span id="L-175"><a href="#L-175"><span class="linenos">175</span></a>              <span class="n">range_a</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
 </span><span id="L-176"><a href="#L-176"><span class="linenos">176</span></a>              <span class="n">range_b</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-177"><a href="#L-177"><span class="linenos">177</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Expanding Factored Binomial</span>
+</span><span id="L-177"><a href="#L-177"><span class="linenos">177</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Expanding Factored Binomial</span>
 </span><span id="L-178"><a href="#L-178"><span class="linenos">178</span></a>
 </span><span id="L-179"><a href="#L-179"><span class="linenos">179</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-180"><a href="#L-180"><span class="linenos">180</span></a><span class="sd">    | --- | --- |</span>
@@ -365,7 +368,7 @@
 </span><span id="L-224"><a href="#L-224"><span class="linenos">224</span></a>
 </span><span id="L-225"><a href="#L-225"><span class="linenos">225</span></a>
 </span><span id="L-226"><a href="#L-226"><span class="linenos">226</span></a><span class="k">def</span> <span class="nf">factoring</span><span class="p">(</span><span class="n">range_x1</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">range_x2</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-227"><a href="#L-227"><span class="linenos">227</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Factoring Quadratic</span>
+</span><span id="L-227"><a href="#L-227"><span class="linenos">227</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Factoring Quadratic</span>
 </span><span id="L-228"><a href="#L-228"><span class="linenos">228</span></a><span class="sd">    Given a quadratic equation in the form x^2 + bx + c, factor it into it&#39;s roots (x - x1)(x -x2)</span>
 </span><span id="L-229"><a href="#L-229"><span class="linenos">229</span></a>
 </span><span id="L-230"><a href="#L-230"><span class="linenos">230</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
@@ -400,7 +403,7 @@
 </span><span id="L-259"><a href="#L-259"><span class="linenos">259</span></a>
 </span><span id="L-260"><a href="#L-260"><span class="linenos">260</span></a>
 </span><span id="L-261"><a href="#L-261"><span class="linenos">261</span></a><span class="k">def</span> <span class="nf">int_matrix_22_determinant</span><span class="p">(</span><span class="n">max_matrix_val</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="L-262"><a href="#L-262"><span class="linenos">262</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Determinant to 2x2 Matrix</span>
+</span><span id="L-262"><a href="#L-262"><span class="linenos">262</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Determinant to 2x2 Matrix</span>
 </span><span id="L-263"><a href="#L-263"><span class="linenos">263</span></a>
 </span><span id="L-264"><a href="#L-264"><span class="linenos">264</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-265"><a href="#L-265"><span class="linenos">265</span></a><span class="sd">    | --- | --- |</span>
@@ -425,14 +428,14 @@
 </span><span id="L-284"><a href="#L-284"><span class="linenos">284</span></a>                              <span class="n">max_b</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
 </span><span id="L-285"><a href="#L-285"><span class="linenos">285</span></a>                              <span class="n">min_denominator</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
 </span><span id="L-286"><a href="#L-286"><span class="linenos">286</span></a>                              <span class="n">max_denominator</span><span class="o">=</span><span class="mi">6</span><span class="p">):</span>
-</span><span id="L-287"><a href="#L-287"><span class="linenos">287</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Intersection of two lines</span>
+</span><span id="L-287"><a href="#L-287"><span class="linenos">287</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Intersection of two lines</span>
 </span><span id="L-288"><a href="#L-288"><span class="linenos">288</span></a>
 </span><span id="L-289"><a href="#L-289"><span class="linenos">289</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-290"><a href="#L-290"><span class="linenos">290</span></a><span class="sd">    | --- | --- |</span>
 </span><span id="L-291"><a href="#L-291"><span class="linenos">291</span></a><span class="sd">    | Find the point of intersection of the two lines: $y = \frac{-2}{6}x + 3$ and $y = \frac{3}{6}x - 8$ | $(\frac{66}{5}, \frac{-7}{5})$ |</span>
 </span><span id="L-292"><a href="#L-292"><span class="linenos">292</span></a><span class="sd">    &quot;&quot;&quot;</span>
 </span><span id="L-293"><a href="#L-293"><span class="linenos">293</span></a>    <span class="k">def</span> <span class="nf">generateEquationString</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
-</span><span id="L-294"><a href="#L-294"><span class="linenos">294</span></a>        <span class="sd">&quot;&quot;&quot;</span>
+</span><span id="L-294"><a href="#L-294"><span class="linenos">294</span></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 </span><span id="L-295"><a href="#L-295"><span class="linenos">295</span></a><span class="sd">        Generates an equation given the slope and intercept.</span>
 </span><span id="L-296"><a href="#L-296"><span class="linenos">296</span></a><span class="sd">        It handles cases where m is fractional.</span>
 </span><span id="L-297"><a href="#L-297"><span class="linenos">297</span></a><span class="sd">        It also ensures that we don&#39;t have weird signs such as y = mx + -b.</span>
@@ -460,9 +463,9 @@
 </span><span id="L-319"><a href="#L-319"><span class="linenos">319</span></a>                <span class="k">return</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2"> + </span><span class="si">{</span><span class="n">b</span><span class="si">}</span><span class="s2">&quot;</span>
 </span><span id="L-320"><a href="#L-320"><span class="linenos">320</span></a>        <span class="k">elif</span> <span class="n">b</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">:</span>
 </span><span id="L-321"><a href="#L-321"><span class="linenos">321</span></a>            <span class="k">if</span> <span class="n">m</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
-</span><span id="L-322"><a href="#L-322"><span class="linenos">322</span></a>                <span class="k">return</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2"> -</span><span class="si">{</span><span class="n">b</span> <span class="o">*</span> <span class="o">-</span><span class="mi">1</span><span class="si">}</span><span class="s2">&quot;</span>
+</span><span id="L-322"><a href="#L-322"><span class="linenos">322</span></a>                <span class="k">return</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2"> -</span><span class="si">{</span><span class="n">b</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="si">}</span><span class="s2">&quot;</span>
 </span><span id="L-323"><a href="#L-323"><span class="linenos">323</span></a>            <span class="k">else</span><span class="p">:</span>
-</span><span id="L-324"><a href="#L-324"><span class="linenos">324</span></a>                <span class="k">return</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2"> - </span><span class="si">{</span><span class="n">b</span> <span class="o">*</span> <span class="o">-</span><span class="mi">1</span><span class="si">}</span><span class="s2">&quot;</span>
+</span><span id="L-324"><a href="#L-324"><span class="linenos">324</span></a>                <span class="k">return</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2"> - </span><span class="si">{</span><span class="n">b</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="si">}</span><span class="s2">&quot;</span>
 </span><span id="L-325"><a href="#L-325"><span class="linenos">325</span></a>        <span class="k">else</span><span class="p">:</span>
 </span><span id="L-326"><a href="#L-326"><span class="linenos">326</span></a>            <span class="k">if</span> <span class="n">m</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
 </span><span id="L-327"><a href="#L-327"><span class="linenos">327</span></a>                <span class="k">return</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2"> 0&quot;</span>
@@ -470,7 +473,7 @@
 </span><span id="L-329"><a href="#L-329"><span class="linenos">329</span></a>                <span class="k">return</span> <span class="n">base</span>
 </span><span id="L-330"><a href="#L-330"><span class="linenos">330</span></a>
 </span><span id="L-331"><a href="#L-331"><span class="linenos">331</span></a>    <span class="k">def</span> <span class="nf">fractionToString</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
-</span><span id="L-332"><a href="#L-332"><span class="linenos">332</span></a>        <span class="sd">&quot;&quot;&quot;</span>
+</span><span id="L-332"><a href="#L-332"><span class="linenos">332</span></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 </span><span id="L-333"><a href="#L-333"><span class="linenos">333</span></a><span class="sd">        Converts the given fractions.Fraction into a string.</span>
 </span><span id="L-334"><a href="#L-334"><span class="linenos">334</span></a><span class="sd">        &quot;&quot;&quot;</span>
 </span><span id="L-335"><a href="#L-335"><span class="linenos">335</span></a>        <span class="k">if</span> <span class="n">x</span><span class="o">.</span><span class="n">denominator</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
@@ -512,7 +515,7 @@
 </span><span id="L-371"><a href="#L-371"><span class="linenos">371</span></a><span class="k">def</span> <span class="nf">invert_matrix</span><span class="p">(</span><span class="n">square_matrix_dimension</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span>
 </span><span id="L-372"><a href="#L-372"><span class="linenos">372</span></a>                  <span class="n">max_matrix_element</span><span class="o">=</span><span class="mi">99</span><span class="p">,</span>
 </span><span id="L-373"><a href="#L-373"><span class="linenos">373</span></a>                  <span class="n">only_integer_elements_in_inverted_matrixe</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-</span><span id="L-374"><a href="#L-374"><span class="linenos">374</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Invert Matrix</span>
+</span><span id="L-374"><a href="#L-374"><span class="linenos">374</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Invert Matrix</span>
 </span><span id="L-375"><a href="#L-375"><span class="linenos">375</span></a>
 </span><span id="L-376"><a href="#L-376"><span class="linenos">376</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-377"><a href="#L-377"><span class="linenos">377</span></a><span class="sd">    | --- | --- |</span>
@@ -593,7 +596,7 @@
 </span><span id="L-452"><a href="#L-452"><span class="linenos">452</span></a>
 </span><span id="L-453"><a href="#L-453"><span class="linenos">453</span></a>
 </span><span id="L-454"><a href="#L-454"><span class="linenos">454</span></a><span class="k">def</span> <span class="nf">linear_equations</span><span class="p">(</span><span class="n">n</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">var_range</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">coeff_range</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="L-455"><a href="#L-455"><span class="linenos">455</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Linear Equations</span>
+</span><span id="L-455"><a href="#L-455"><span class="linenos">455</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Linear Equations</span>
 </span><span id="L-456"><a href="#L-456"><span class="linenos">456</span></a>
 </span><span id="L-457"><a href="#L-457"><span class="linenos">457</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-458"><a href="#L-458"><span class="linenos">458</span></a><span class="sd">    | --- | --- |</span>
@@ -629,7 +632,7 @@
 </span><span id="L-488"><a href="#L-488"><span class="linenos">488</span></a>
 </span><span id="L-489"><a href="#L-489"><span class="linenos">489</span></a>
 </span><span id="L-490"><a href="#L-490"><span class="linenos">490</span></a><span class="k">def</span> <span class="nf">line_equation_from_2_points</span><span class="p">(</span><span class="n">max_val</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="L-491"><a href="#L-491"><span class="linenos">491</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Equation of Line from Two Points</span>
+</span><span id="L-491"><a href="#L-491"><span class="linenos">491</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Equation of Line from Two Points</span>
 </span><span id="L-492"><a href="#L-492"><span class="linenos">492</span></a>
 </span><span id="L-493"><a href="#L-493"><span class="linenos">493</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-494"><a href="#L-494"><span class="linenos">494</span></a><span class="sd">    | --- | --- |</span>
@@ -645,11 +648,11 @@
 </span><span id="L-504"><a href="#L-504"><span class="linenos">504</span></a>    <span class="n">m2</span> <span class="o">=</span> <span class="p">(</span><span class="n">x2</span> <span class="o">-</span> <span class="n">x1</span><span class="p">)</span> <span class="o">//</span> <span class="n">math</span><span class="o">.</span><span class="n">gcd</span><span class="p">(</span><span class="n">y2</span> <span class="o">-</span> <span class="n">y1</span><span class="p">,</span> <span class="n">x2</span> <span class="o">-</span> <span class="n">x1</span><span class="p">)</span>
 </span><span id="L-505"><a href="#L-505"><span class="linenos">505</span></a>    <span class="n">c1</span> <span class="o">=</span> <span class="p">(</span><span class="n">y1</span> <span class="o">*</span> <span class="p">(</span><span class="n">x2</span> <span class="o">-</span> <span class="n">x1</span><span class="p">)</span> <span class="o">-</span> <span class="p">(</span><span class="n">y2</span> <span class="o">-</span> <span class="n">y1</span><span class="p">)</span> <span class="o">*</span> <span class="n">x1</span><span class="p">)</span> <span class="o">//</span> <span class="n">math</span><span class="o">.</span><span class="n">gcd</span><span class="p">(</span><span class="n">y1</span> <span class="o">*</span> <span class="p">(</span><span class="n">x2</span> <span class="o">-</span> <span class="n">x1</span><span class="p">)</span> <span class="o">-</span> <span class="p">(</span><span class="n">y2</span> <span class="o">-</span> <span class="n">y1</span><span class="p">)</span> <span class="o">*</span> <span class="n">x1</span><span class="p">,</span> <span class="p">(</span><span class="n">x2</span> <span class="o">-</span> <span class="n">x1</span><span class="p">))</span>
 </span><span id="L-506"><a href="#L-506"><span class="linenos">506</span></a>    <span class="n">c2</span> <span class="o">=</span> <span class="p">(</span><span class="n">x2</span> <span class="o">-</span> <span class="n">x1</span><span class="p">)</span> <span class="o">//</span> <span class="n">math</span><span class="o">.</span><span class="n">gcd</span><span class="p">(</span><span class="n">y1</span> <span class="o">*</span> <span class="p">(</span><span class="n">x2</span> <span class="o">-</span> <span class="n">x1</span><span class="p">)</span> <span class="o">-</span> <span class="p">(</span><span class="n">y2</span> <span class="o">-</span> <span class="n">y1</span><span class="p">)</span> <span class="o">*</span> <span class="n">x1</span><span class="p">,</span> <span class="p">(</span><span class="n">x2</span> <span class="o">-</span> <span class="n">x1</span><span class="p">))</span>
-</span><span id="L-507"><a href="#L-507"><span class="linenos">507</span></a>    <span class="n">c</span> <span class="o">=</span> <span class="sa">rf</span><span class="s2">&quot;</span><span class="si">{</span><span class="s1">&#39;+&#39;</span> <span class="k">if</span> <span class="n">c1</span> <span class="o">&gt;=</span> <span class="mi">0</span> <span class="k">else</span> <span class="s1">&#39;-&#39;</span><span class="si">}</span><span class="s2">\frac</span><span class="se">{{</span><span class="si">{</span><span class="nb">abs</span><span class="p">(</span><span class="n">c1</span><span class="p">)</span><span class="si">}</span><span class="se">}}{{</span><span class="si">{</span><span class="n">c2</span><span class="si">}</span><span class="se">}}</span><span class="s2">&quot;</span> <span class="k">if</span> <span class="n">c1</span> <span class="o">!=</span> <span class="mi">0</span> <span class="k">else</span> <span class="s2">&quot;&quot;</span>
+</span><span id="L-507"><a href="#L-507"><span class="linenos">507</span></a>    <span class="n">c</span> <span class="o">=</span> <span class="sa">rf</span><span class="s2">&quot;</span><span class="si">{</span><span class="s1">&#39;+&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">c1</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="s1">&#39;-&#39;</span><span class="si">}</span><span class="s2">\frac</span><span class="se">{{</span><span class="si">{</span><span class="nb">abs</span><span class="p">(</span><span class="n">c1</span><span class="p">)</span><span class="si">}</span><span class="se">}}{{</span><span class="si">{</span><span class="n">c2</span><span class="si">}</span><span class="se">}}</span><span class="s2">&quot;</span> <span class="k">if</span> <span class="n">c1</span> <span class="o">!=</span> <span class="mi">0</span> <span class="k">else</span> <span class="s2">&quot;&quot;</span>
 </span><span id="L-508"><a href="#L-508"><span class="linenos">508</span></a>    <span class="k">if</span> <span class="n">c2</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">:</span>
 </span><span id="L-509"><a href="#L-509"><span class="linenos">509</span></a>        <span class="n">c2</span> <span class="o">=</span> <span class="o">-</span><span class="n">c2</span>
 </span><span id="L-510"><a href="#L-510"><span class="linenos">510</span></a>        <span class="n">c1</span> <span class="o">=</span> <span class="o">-</span><span class="n">c1</span>
-</span><span id="L-511"><a href="#L-511"><span class="linenos">511</span></a>        <span class="n">c</span> <span class="o">=</span> <span class="sa">rf</span><span class="s2">&quot;</span><span class="si">{</span><span class="s1">&#39;+&#39;</span> <span class="k">if</span> <span class="n">c1</span> <span class="o">&gt;=</span> <span class="mi">0</span> <span class="k">else</span> <span class="s1">&#39;-&#39;</span><span class="si">}</span><span class="s2">\frac</span><span class="se">{{</span><span class="si">{</span><span class="nb">abs</span><span class="p">(</span><span class="n">c1</span><span class="p">)</span><span class="si">}</span><span class="se">}}{{</span><span class="si">{</span><span class="n">c2</span><span class="si">}</span><span class="se">}}</span><span class="s2">&quot;</span>
+</span><span id="L-511"><a href="#L-511"><span class="linenos">511</span></a>        <span class="n">c</span> <span class="o">=</span> <span class="sa">rf</span><span class="s2">&quot;</span><span class="si">{</span><span class="s1">&#39;+&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">c1</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="s1">&#39;-&#39;</span><span class="si">}</span><span class="s2">\frac</span><span class="se">{{</span><span class="si">{</span><span class="nb">abs</span><span class="p">(</span><span class="n">c1</span><span class="p">)</span><span class="si">}</span><span class="se">}}{{</span><span class="si">{</span><span class="n">c2</span><span class="si">}</span><span class="se">}}</span><span class="s2">&quot;</span>
 </span><span id="L-512"><a href="#L-512"><span class="linenos">512</span></a>    <span class="k">if</span> <span class="n">c2</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
 </span><span id="L-513"><a href="#L-513"><span class="linenos">513</span></a>        <span class="n">c</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">c1</span><span class="si">:</span><span class="s2">+</span><span class="si">}</span><span class="s2">&quot;</span>
 </span><span id="L-514"><a href="#L-514"><span class="linenos">514</span></a>
@@ -671,7 +674,7 @@
 </span><span id="L-530"><a href="#L-530"><span class="linenos">530</span></a>
 </span><span id="L-531"><a href="#L-531"><span class="linenos">531</span></a>
 </span><span id="L-532"><a href="#L-532"><span class="linenos">532</span></a><span class="k">def</span> <span class="nf">log</span><span class="p">(</span><span class="n">max_base</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">max_val</span><span class="o">=</span><span class="mi">8</span><span class="p">):</span>
-</span><span id="L-533"><a href="#L-533"><span class="linenos">533</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Logarithm</span>
+</span><span id="L-533"><a href="#L-533"><span class="linenos">533</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Logarithm</span>
 </span><span id="L-534"><a href="#L-534"><span class="linenos">534</span></a>
 </span><span id="L-535"><a href="#L-535"><span class="linenos">535</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-536"><a href="#L-536"><span class="linenos">536</span></a><span class="sd">    | --- | --- |</span>
@@ -687,7 +690,7 @@
 </span><span id="L-546"><a href="#L-546"><span class="linenos">546</span></a>
 </span><span id="L-547"><a href="#L-547"><span class="linenos">547</span></a>
 </span><span id="L-548"><a href="#L-548"><span class="linenos">548</span></a><span class="k">def</span> <span class="nf">matrix_multiplication</span><span class="p">(</span><span class="n">max_val</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">max_dim</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-549"><a href="#L-549"><span class="linenos">549</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Multiply Two Matrices</span>
+</span><span id="L-549"><a href="#L-549"><span class="linenos">549</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Multiply Two Matrices</span>
 </span><span id="L-550"><a href="#L-550"><span class="linenos">550</span></a>
 </span><span id="L-551"><a href="#L-551"><span class="linenos">551</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-552"><a href="#L-552"><span class="linenos">552</span></a><span class="sd">    | --- | --- |</span>
@@ -718,7 +721,7 @@
 </span><span id="L-577"><a href="#L-577"><span class="linenos">577</span></a>
 </span><span id="L-578"><a href="#L-578"><span class="linenos">578</span></a>
 </span><span id="L-579"><a href="#L-579"><span class="linenos">579</span></a><span class="k">def</span> <span class="nf">midpoint_of_two_points</span><span class="p">(</span><span class="n">max_value</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="L-580"><a href="#L-580"><span class="linenos">580</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Midpoint of two points</span>
+</span><span id="L-580"><a href="#L-580"><span class="linenos">580</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Midpoint of two points</span>
 </span><span id="L-581"><a href="#L-581"><span class="linenos">581</span></a>
 </span><span id="L-582"><a href="#L-582"><span class="linenos">582</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-583"><a href="#L-583"><span class="linenos">583</span></a><span class="sd">    | --- | --- |</span>
@@ -738,7 +741,7 @@
 </span><span id="L-597"><a href="#L-597"><span class="linenos">597</span></a>
 </span><span id="L-598"><a href="#L-598"><span class="linenos">598</span></a><span class="k">def</span> <span class="nf">multiply_complex_numbers</span><span class="p">(</span><span class="n">min_real_imaginary_num</span><span class="o">=-</span><span class="mi">20</span><span class="p">,</span>
 </span><span id="L-599"><a href="#L-599"><span class="linenos">599</span></a>                             <span class="n">max_real_imaginary_num</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="L-600"><a href="#L-600"><span class="linenos">600</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Multiplication of 2 complex numbers</span>
+</span><span id="L-600"><a href="#L-600"><span class="linenos">600</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Multiplication of 2 complex numbers</span>
 </span><span id="L-601"><a href="#L-601"><span class="linenos">601</span></a>
 </span><span id="L-602"><a href="#L-602"><span class="linenos">602</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-603"><a href="#L-603"><span class="linenos">603</span></a><span class="sd">    | --- | --- |</span>
@@ -756,7 +759,7 @@
 </span><span id="L-615"><a href="#L-615"><span class="linenos">615</span></a>
 </span><span id="L-616"><a href="#L-616"><span class="linenos">616</span></a>
 </span><span id="L-617"><a href="#L-617"><span class="linenos">617</span></a><span class="k">def</span> <span class="nf">multiply_int_to_22_matrix</span><span class="p">(</span><span class="n">max_matrix_val</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">max_res</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="L-618"><a href="#L-618"><span class="linenos">618</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Multiply Integer to 2x2 Matrix</span>
+</span><span id="L-618"><a href="#L-618"><span class="linenos">618</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Multiply Integer to 2x2 Matrix</span>
 </span><span id="L-619"><a href="#L-619"><span class="linenos">619</span></a>
 </span><span id="L-620"><a href="#L-620"><span class="linenos">620</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-621"><a href="#L-621"><span class="linenos">621</span></a><span class="sd">    | --- | --- |</span>
@@ -782,7 +785,7 @@
 </span><span id="L-641"><a href="#L-641"><span class="linenos">641</span></a>
 </span><span id="L-642"><a href="#L-642"><span class="linenos">642</span></a>
 </span><span id="L-643"><a href="#L-643"><span class="linenos">643</span></a><span class="k">def</span> <span class="nf">quadratic_equation</span><span class="p">(</span><span class="n">max_val</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="L-644"><a href="#L-644"><span class="linenos">644</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Quadratic Equation</span>
+</span><span id="L-644"><a href="#L-644"><span class="linenos">644</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Quadratic Equation</span>
 </span><span id="L-645"><a href="#L-645"><span class="linenos">645</span></a>
 </span><span id="L-646"><a href="#L-646"><span class="linenos">646</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-647"><a href="#L-647"><span class="linenos">647</span></a><span class="sd">    | --- | --- |</span>
@@ -803,7 +806,7 @@
 </span><span id="L-662"><a href="#L-662"><span class="linenos">662</span></a><span class="k">def</span> <span class="nf">simple_interest</span><span class="p">(</span><span class="n">max_principle</span><span class="o">=</span><span class="mi">10000</span><span class="p">,</span>
 </span><span id="L-663"><a href="#L-663"><span class="linenos">663</span></a>                    <span class="n">max_rate</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
 </span><span id="L-664"><a href="#L-664"><span class="linenos">664</span></a>                    <span class="n">max_time</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-665"><a href="#L-665"><span class="linenos">665</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Simple Interest</span>
+</span><span id="L-665"><a href="#L-665"><span class="linenos">665</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Simple Interest</span>
 </span><span id="L-666"><a href="#L-666"><span class="linenos">666</span></a>
 </span><span id="L-667"><a href="#L-667"><span class="linenos">667</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-668"><a href="#L-668"><span class="linenos">668</span></a><span class="sd">    | --- | --- |</span>
@@ -822,7 +825,7 @@
 </span><span id="L-681"><a href="#L-681"><span class="linenos">681</span></a><span class="k">def</span> <span class="nf">system_of_equations</span><span class="p">(</span><span class="n">range_x</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
 </span><span id="L-682"><a href="#L-682"><span class="linenos">682</span></a>                        <span class="n">range_y</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
 </span><span id="L-683"><a href="#L-683"><span class="linenos">683</span></a>                        <span class="n">coeff_mult_range</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-684"><a href="#L-684"><span class="linenos">684</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Solve a System of Equations in R^2</span>
+</span><span id="L-684"><a href="#L-684"><span class="linenos">684</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Solve a System of Equations in R^2</span>
 </span><span id="L-685"><a href="#L-685"><span class="linenos">685</span></a>
 </span><span id="L-686"><a href="#L-686"><span class="linenos">686</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-687"><a href="#L-687"><span class="linenos">687</span></a><span class="sd">    | --- | --- |</span>
@@ -874,7 +877,7 @@
 </span><span id="L-733"><a href="#L-733"><span class="linenos">733</span></a>
 </span><span id="L-734"><a href="#L-734"><span class="linenos">734</span></a>
 </span><span id="L-735"><a href="#L-735"><span class="linenos">735</span></a><span class="k">def</span> <span class="nf">vector_cross</span><span class="p">(</span><span class="n">min_val</span><span class="o">=-</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_val</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="L-736"><a href="#L-736"><span class="linenos">736</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Cross product of 2 vectors</span>
+</span><span id="L-736"><a href="#L-736"><span class="linenos">736</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Cross product of 2 vectors</span>
 </span><span id="L-737"><a href="#L-737"><span class="linenos">737</span></a>
 </span><span id="L-738"><a href="#L-738"><span class="linenos">738</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-739"><a href="#L-739"><span class="linenos">739</span></a><span class="sd">    | --- | --- |</span>
@@ -893,7 +896,7 @@
 </span><span id="L-752"><a href="#L-752"><span class="linenos">752</span></a>
 </span><span id="L-753"><a href="#L-753"><span class="linenos">753</span></a>
 </span><span id="L-754"><a href="#L-754"><span class="linenos">754</span></a><span class="k">def</span> <span class="nf">vector_dot</span><span class="p">(</span><span class="n">min_val</span><span class="o">=-</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_val</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="L-755"><a href="#L-755"><span class="linenos">755</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Dot product of 2 vectors</span>
+</span><span id="L-755"><a href="#L-755"><span class="linenos">755</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Dot product of 2 vectors</span>
 </span><span id="L-756"><a href="#L-756"><span class="linenos">756</span></a>
 </span><span id="L-757"><a href="#L-757"><span class="linenos">757</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-758"><a href="#L-758"><span class="linenos">758</span></a><span class="sd">    | --- | --- |</span>
@@ -906,6 +909,30 @@
 </span><span id="L-765"><a href="#L-765"><span class="linenos">765</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;$</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="s1">\cdot</span><span class="si">{</span><span class="n">b</span><span class="si">}</span><span class="s1">=$&#39;</span>
 </span><span id="L-766"><a href="#L-766"><span class="linenos">766</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="n">c</span><span class="si">}</span><span class="s1">$&#39;</span>
 </span><span id="L-767"><a href="#L-767"><span class="linenos">767</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
+</span><span id="L-768"><a href="#L-768"><span class="linenos">768</span></a>
+</span><span id="L-769"><a href="#L-769"><span class="linenos">769</span></a>
+</span><span id="L-770"><a href="#L-770"><span class="linenos">770</span></a><span class="k">def</span> <span class="nf">orthogonal_projection</span><span class="p">(</span><span class="n">min_val</span><span class="o">=-</span><span class="mi">10</span><span class="p">,</span> <span class="n">max_val</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
+</span><span id="L-771"><a href="#L-771"><span class="linenos">771</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Orthogonal Projection</span>
+</span><span id="L-772"><a href="#L-772"><span class="linenos">772</span></a>
+</span><span id="L-773"><a href="#L-773"><span class="linenos">773</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
+</span><span id="L-774"><a href="#L-774"><span class="linenos">774</span></a><span class="sd">    | --- | --- |</span>
+</span><span id="L-775"><a href="#L-775"><span class="linenos">775</span></a><span class="sd">    | Find the orthogonal projection of $[2, 3]$ onto $[4, -7]$ | $[\frac{-4}{5}, \frac{7}{5}]$ |</span>
+</span><span id="L-776"><a href="#L-776"><span class="linenos">776</span></a><span class="sd">    &quot;&quot;&quot;</span>
+</span><span id="L-777"><a href="#L-777"><span class="linenos">777</span></a>    <span class="n">v</span> <span class="o">=</span> <span class="p">[</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="n">min_val</span><span class="p">,</span> <span class="n">max_val</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">)]</span>
+</span><span id="L-778"><a href="#L-778"><span class="linenos">778</span></a>    <span class="n">u</span> <span class="o">=</span> <span class="p">[</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="n">min_val</span><span class="p">,</span> <span class="n">max_val</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">)]</span>
+</span><span id="L-779"><a href="#L-779"><span class="linenos">779</span></a>    <span class="n">dot_t</span> <span class="o">=</span> <span class="n">v</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">u</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">u</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+</span><span id="L-780"><a href="#L-780"><span class="linenos">780</span></a>    <span class="n">dot_b</span> <span class="o">=</span> <span class="n">u</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">u</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">u</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">u</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+</span><span id="L-781"><a href="#L-781"><span class="linenos">781</span></a>    <span class="n">frac</span> <span class="o">=</span> <span class="n">fractions</span><span class="o">.</span><span class="n">Fraction</span><span class="p">(</span><span class="n">dot_t</span><span class="p">,</span> <span class="n">dot_b</span><span class="p">)</span><span class="o">.</span><span class="n">limit_denominator</span><span class="p">()</span>
+</span><span id="L-782"><a href="#L-782"><span class="linenos">782</span></a>    <span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="n">frac</span> <span class="o">*</span> <span class="n">u</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">frac</span> <span class="o">*</span> <span class="n">u</span><span class="p">[</span><span class="mi">1</span><span class="p">]]</span>
+</span><span id="L-783"><a href="#L-783"><span class="linenos">783</span></a>
+</span><span id="L-784"><a href="#L-784"><span class="linenos">784</span></a>    <span class="k">if</span> <span class="n">y</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">denominator</span> <span class="o">!=</span> <span class="mi">1</span><span class="p">:</span>
+</span><span id="L-785"><a href="#L-785"><span class="linenos">785</span></a>        <span class="n">y</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;\frac</span><span class="se">{{</span><span class="si">{</span><span class="n">y</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">numerator</span><span class="si">}</span><span class="se">}}{{</span><span class="si">{</span><span class="n">y</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">denominator</span><span class="si">}</span><span class="se">}}</span><span class="s1">&#39;</span>
+</span><span id="L-786"><a href="#L-786"><span class="linenos">786</span></a>    <span class="k">if</span> <span class="n">y</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">denominator</span> <span class="o">!=</span> <span class="mi">1</span><span class="p">:</span>
+</span><span id="L-787"><a href="#L-787"><span class="linenos">787</span></a>        <span class="n">y</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;\frac</span><span class="se">{{</span><span class="si">{</span><span class="n">y</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">numerator</span><span class="si">}</span><span class="se">}}{{</span><span class="si">{</span><span class="n">y</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">denominator</span><span class="si">}</span><span class="se">}}</span><span class="s1">&#39;</span>
+</span><span id="L-788"><a href="#L-788"><span class="linenos">788</span></a>
+</span><span id="L-789"><a href="#L-789"><span class="linenos">789</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;Find the orthogonal projection of $</span><span class="si">{</span><span class="n">v</span><span class="si">}</span><span class="s1">$ onto $</span><span class="si">{</span><span class="n">u</span><span class="si">}</span><span class="s1">$&#39;</span>
+</span><span id="L-790"><a href="#L-790"><span class="linenos">790</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$[</span><span class="si">{</span><span class="n">y</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="si">}</span><span class="s1">, </span><span class="si">{</span><span class="n">y</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="si">}</span><span class="s1">]$&#39;</span>
+</span><span id="L-791"><a href="#L-791"><span class="linenos">791</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span></pre></div>
 
 
@@ -922,7 +949,7 @@
     </div>
     <a class="headerlink" href="#basic_algebra"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="basic_algebra-9"><a href="#basic_algebra-9"><span class="linenos"> 9</span></a><span class="k">def</span> <span class="nf">basic_algebra</span><span class="p">(</span><span class="n">max_variable</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="basic_algebra-10"><a href="#basic_algebra-10"><span class="linenos">10</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Basic Algebra</span>
+</span><span id="basic_algebra-10"><a href="#basic_algebra-10"><span class="linenos">10</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Basic Algebra</span>
 </span><span id="basic_algebra-11"><a href="#basic_algebra-11"><span class="linenos">11</span></a>
 </span><span id="basic_algebra-12"><a href="#basic_algebra-12"><span class="linenos">12</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="basic_algebra-13"><a href="#basic_algebra-13"><span class="linenos">13</span></a><span class="sd">    | --- | --- |</span>
@@ -939,12 +966,12 @@
 </span><span id="basic_algebra-24"><a href="#basic_algebra-24"><span class="linenos">24</span></a>        <span class="k">return</span> <span class="n">x</span>
 </span><span id="basic_algebra-25"><a href="#basic_algebra-25"><span class="linenos">25</span></a>
 </span><span id="basic_algebra-26"><a href="#basic_algebra-26"><span class="linenos">26</span></a>    <span class="n">i</span> <span class="o">=</span> <span class="n">calculate_gcd</span><span class="p">((</span><span class="n">c</span> <span class="o">-</span> <span class="n">b</span><span class="p">),</span> <span class="n">a</span><span class="p">)</span>
-</span><span id="basic_algebra-27"><a href="#basic_algebra-27"><span class="linenos">27</span></a>    <span class="n">x</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="p">(</span><span class="n">c</span> <span class="o">-</span> <span class="n">b</span><span class="p">)</span><span class="o">//</span><span class="n">i</span><span class="si">}</span><span class="s2">/</span><span class="si">{</span><span class="n">a</span><span class="o">//</span><span class="n">i</span><span class="si">}</span><span class="s2">&quot;</span>
+</span><span id="basic_algebra-27"><a href="#basic_algebra-27"><span class="linenos">27</span></a>    <span class="n">x</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="p">(</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">b</span><span class="p">)</span><span class="o">//</span><span class="n">i</span><span class="si">}</span><span class="s2">/</span><span class="si">{</span><span class="n">a</span><span class="o">//</span><span class="n">i</span><span class="si">}</span><span class="s2">&quot;</span>
 </span><span id="basic_algebra-28"><a href="#basic_algebra-28"><span class="linenos">28</span></a>
 </span><span id="basic_algebra-29"><a href="#basic_algebra-29"><span class="linenos">29</span></a>    <span class="k">if</span> <span class="p">(</span><span class="n">c</span> <span class="o">-</span> <span class="n">b</span> <span class="o">==</span> <span class="mi">0</span><span class="p">):</span>
 </span><span id="basic_algebra-30"><a href="#basic_algebra-30"><span class="linenos">30</span></a>        <span class="n">x</span> <span class="o">=</span> <span class="s2">&quot;0&quot;</span>
 </span><span id="basic_algebra-31"><a href="#basic_algebra-31"><span class="linenos">31</span></a>    <span class="k">elif</span> <span class="n">a</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">a</span> <span class="o">==</span> <span class="n">i</span><span class="p">:</span>
-</span><span id="basic_algebra-32"><a href="#basic_algebra-32"><span class="linenos">32</span></a>        <span class="n">x</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">c</span> <span class="o">-</span> <span class="n">b</span><span class="si">}</span><span class="s2">&quot;</span>
+</span><span id="basic_algebra-32"><a href="#basic_algebra-32"><span class="linenos">32</span></a>        <span class="n">x</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">b</span><span class="si">}</span><span class="s2">&quot;</span>
 </span><span id="basic_algebra-33"><a href="#basic_algebra-33"><span class="linenos">33</span></a>
 </span><span id="basic_algebra-34"><a href="#basic_algebra-34"><span class="linenos">34</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="s2">x + </span><span class="si">{</span><span class="n">b</span><span class="si">}</span><span class="s2"> = </span><span class="si">{</span><span class="n">c</span><span class="si">}</span><span class="s2">$&quot;</span>
 </span><span id="basic_algebra-35"><a href="#basic_algebra-35"><span class="linenos">35</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">x</span><span class="si">}</span><span class="s2">$&quot;</span>
@@ -984,7 +1011,7 @@
     </div>
     <a class="headerlink" href="#combine_like_terms"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="combine_like_terms-39"><a href="#combine_like_terms-39"><span class="linenos">39</span></a><span class="k">def</span> <span class="nf">combine_like_terms</span><span class="p">(</span><span class="n">max_coef</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">max_exp</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_terms</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="combine_like_terms-40"><a href="#combine_like_terms-40"><span class="linenos">40</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Combine Like Terms</span>
+</span><span id="combine_like_terms-40"><a href="#combine_like_terms-40"><span class="linenos">40</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Combine Like Terms</span>
 </span><span id="combine_like_terms-41"><a href="#combine_like_terms-41"><span class="linenos">41</span></a>
 </span><span id="combine_like_terms-42"><a href="#combine_like_terms-42"><span class="linenos">42</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="combine_like_terms-43"><a href="#combine_like_terms-43"><span class="linenos">43</span></a><span class="sd">    | --- | --- |</span>
@@ -1041,11 +1068,11 @@
     </div>
     <a class="headerlink" href="#complex_quadratic"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="complex_quadratic-64"><a href="#complex_quadratic-64"><span class="linenos"> 64</span></a><span class="k">def</span> <span class="nf">complex_quadratic</span><span class="p">(</span><span class="n">prob_type</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_range</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="complex_quadratic-65"><a href="#complex_quadratic-65"><span class="linenos"> 65</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Complex Quadratic Equation</span>
+</span><span id="complex_quadratic-65"><a href="#complex_quadratic-65"><span class="linenos"> 65</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Complex Quadratic Equation</span>
 </span><span id="complex_quadratic-66"><a href="#complex_quadratic-66"><span class="linenos"> 66</span></a>
 </span><span id="complex_quadratic-67"><a href="#complex_quadratic-67"><span class="linenos"> 67</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="complex_quadratic-68"><a href="#complex_quadratic-68"><span class="linenos"> 68</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="complex_quadratic-69"><a href="#complex_quadratic-69"><span class="linenos"> 69</span></a><span class="sd">    | Find the roots of given Quadratic Equation $x^2 + 8x + 8 = 0$ | $((-1.172, -6.828)) = (\frac{-8 + \sqrt{32}}{2*1}, (\frac{-8 - \sqrt{32}}{2*1})$ |</span>
+</span><span id="complex_quadratic-69"><a href="#complex_quadratic-69"><span class="linenos"> 69</span></a><span class="sd">    | Find the roots of given Quadratic Equation $x^2 + 8x + 8 = 0$ | $((-1.172, -6.828)) = (\frac{-8 + \sqrt{32}}{2}, (\frac{-8 - \sqrt{32}}{2})$ |</span>
 </span><span id="complex_quadratic-70"><a href="#complex_quadratic-70"><span class="linenos"> 70</span></a><span class="sd">    &quot;&quot;&quot;</span>
 </span><span id="complex_quadratic-71"><a href="#complex_quadratic-71"><span class="linenos"> 71</span></a>    <span class="k">if</span> <span class="n">prob_type</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">prob_type</span> <span class="o">&gt;</span> <span class="mi">1</span><span class="p">:</span>
 </span><span id="complex_quadratic-72"><a href="#complex_quadratic-72"><span class="linenos"> 72</span></a>        <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;prob_type not supported&quot;</span><span class="p">)</span>
@@ -1090,9 +1117,9 @@
 </span><span id="complex_quadratic-111"><a href="#complex_quadratic-111"><span class="linenos">111</span></a>
 </span><span id="complex_quadratic-112"><a href="#complex_quadratic-112"><span class="linenos">112</span></a>        <span class="k">if</span> <span class="n">sqrt_d</span> <span class="o">-</span> <span class="nb">int</span><span class="p">(</span><span class="n">sqrt_d</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
 </span><span id="complex_quadratic-113"><a href="#complex_quadratic-113"><span class="linenos">113</span></a>            <span class="n">sqrt_d</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">sqrt_d</span><span class="p">)</span>
-</span><span id="complex_quadratic-114"><a href="#complex_quadratic-114"><span class="linenos">114</span></a>            <span class="n">solution</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;(\frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> + </span><span class="si">{</span><span class="n">sqrt_d</span><span class="si">}</span><span class="s1">i</span><span class="se">}}{{</span><span class="s1">2*</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">, \frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> - </span><span class="si">{</span><span class="n">sqrt_d</span><span class="si">}</span><span class="s1">i</span><span class="se">}}{{</span><span class="s1">2*</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">)&#39;</span>
+</span><span id="complex_quadratic-114"><a href="#complex_quadratic-114"><span class="linenos">114</span></a>            <span class="n">solution</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;(\frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> + </span><span class="si">{</span><span class="n">sqrt_d</span><span class="si">}</span><span class="s1">i</span><span class="se">}}{{</span><span class="si">{</span><span class="mi">2</span><span class="o">*</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">, \frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> - </span><span class="si">{</span><span class="n">sqrt_d</span><span class="si">}</span><span class="s1">i</span><span class="se">}}{{</span><span class="si">{</span><span class="mi">2</span><span class="o">*</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">)&#39;</span>
 </span><span id="complex_quadratic-115"><a href="#complex_quadratic-115"><span class="linenos">115</span></a>        <span class="k">else</span><span class="p">:</span>
-</span><span id="complex_quadratic-116"><a href="#complex_quadratic-116"><span class="linenos">116</span></a>            <span class="n">solution</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;(\frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> + \sqrt</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">d</span><span class="si">}</span><span class="se">}}</span><span class="s1">i</span><span class="se">}}{{</span><span class="s1">2*</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">, \frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> - \sqrt</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">d</span><span class="si">}</span><span class="se">}}</span><span class="s1">i</span><span class="se">}}{{</span><span class="s1">2*</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">)&#39;</span>
+</span><span id="complex_quadratic-116"><a href="#complex_quadratic-116"><span class="linenos">116</span></a>            <span class="n">solution</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;(\frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> + \sqrt</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">d</span><span class="si">}</span><span class="se">}}</span><span class="s1">i</span><span class="se">}}{{</span><span class="si">{</span><span class="mi">2</span><span class="o">*</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">, \frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> - \sqrt</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">d</span><span class="si">}</span><span class="se">}}</span><span class="s1">i</span><span class="se">}}{{</span><span class="si">{</span><span class="mi">2</span><span class="o">*</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">)&#39;</span>
 </span><span id="complex_quadratic-117"><a href="#complex_quadratic-117"><span class="linenos">117</span></a>
 </span><span id="complex_quadratic-118"><a href="#complex_quadratic-118"><span class="linenos">118</span></a>        <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span><span id="complex_quadratic-119"><a href="#complex_quadratic-119"><span class="linenos">119</span></a>
@@ -1104,11 +1131,11 @@
 </span><span id="complex_quadratic-125"><a href="#complex_quadratic-125"><span class="linenos">125</span></a>
 </span><span id="complex_quadratic-126"><a href="#complex_quadratic-126"><span class="linenos">126</span></a>        <span class="k">if</span> <span class="n">sqrt_d</span> <span class="o">-</span> <span class="nb">int</span><span class="p">(</span><span class="n">sqrt_d</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
 </span><span id="complex_quadratic-127"><a href="#complex_quadratic-127"><span class="linenos">127</span></a>            <span class="n">sqrt_d</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">sqrt_d</span><span class="p">)</span>
-</span><span id="complex_quadratic-128"><a href="#complex_quadratic-128"><span class="linenos">128</span></a>            <span class="n">g_sol</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;(\frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> + </span><span class="si">{</span><span class="n">sqrt_d</span><span class="si">}</span><span class="se">}}{{</span><span class="s1">2*</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">, \frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> - </span><span class="si">{</span><span class="n">sqrt_d</span><span class="si">}</span><span class="se">}}{{</span><span class="s1">2*</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">)&#39;</span>
+</span><span id="complex_quadratic-128"><a href="#complex_quadratic-128"><span class="linenos">128</span></a>            <span class="n">g_sol</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;(\frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> + </span><span class="si">{</span><span class="n">sqrt_d</span><span class="si">}</span><span class="se">}}{{</span><span class="si">{</span><span class="mi">2</span><span class="o">*</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">, \frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> - </span><span class="si">{</span><span class="n">sqrt_d</span><span class="si">}</span><span class="se">}}{{</span><span class="si">{</span><span class="mi">2</span><span class="o">*</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">)&#39;</span>
 </span><span id="complex_quadratic-129"><a href="#complex_quadratic-129"><span class="linenos">129</span></a>        <span class="k">else</span><span class="p">:</span>
-</span><span id="complex_quadratic-130"><a href="#complex_quadratic-130"><span class="linenos">130</span></a>            <span class="n">g_sol</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;(\frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> + \sqrt</span><span class="se">{{</span><span class="si">{</span><span class="n">d</span><span class="si">}</span><span class="se">}}}}{{</span><span class="s1">2*</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">, (\frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> - \sqrt</span><span class="se">{{</span><span class="si">{</span><span class="n">d</span><span class="si">}</span><span class="se">}}}}{{</span><span class="s1">2*</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">)&#39;</span>
+</span><span id="complex_quadratic-130"><a href="#complex_quadratic-130"><span class="linenos">130</span></a>            <span class="n">g_sol</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;(\frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> + \sqrt</span><span class="se">{{</span><span class="si">{</span><span class="n">d</span><span class="si">}</span><span class="se">}}}}{{</span><span class="si">{</span><span class="mi">2</span><span class="o">*</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">, (\frac</span><span class="se">{{</span><span class="si">{</span><span class="o">-</span><span class="n">b</span><span class="si">}</span><span class="s1"> - \sqrt</span><span class="se">{{</span><span class="si">{</span><span class="n">d</span><span class="si">}</span><span class="se">}}}}{{</span><span class="si">{</span><span class="mi">2</span><span class="o">*</span><span class="n">a</span><span class="si">}</span><span class="se">}}</span><span class="s1">)&#39;</span>
 </span><span id="complex_quadratic-131"><a href="#complex_quadratic-131"><span class="linenos">131</span></a>
-</span><span id="complex_quadratic-132"><a href="#complex_quadratic-132"><span class="linenos">132</span></a>        <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$(</span><span class="si">{</span><span class="n">s_root1</span><span class="p">,</span> <span class="n">s_root2</span><span class="si">}</span><span class="s1">) = </span><span class="si">{</span><span class="n">g_sol</span><span class="si">}</span><span class="s1">$&#39;</span>
+</span><span id="complex_quadratic-132"><a href="#complex_quadratic-132"><span class="linenos">132</span></a>        <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$(</span><span class="si">{</span><span class="n">s_root1</span><span class="p">,</span><span class="w"> </span><span class="n">s_root2</span><span class="si">}</span><span class="s1">) = </span><span class="si">{</span><span class="n">g_sol</span><span class="si">}</span><span class="s1">$&#39;</span>
 </span><span id="complex_quadratic-133"><a href="#complex_quadratic-133"><span class="linenos">133</span></a>
 </span><span id="complex_quadratic-134"><a href="#complex_quadratic-134"><span class="linenos">134</span></a>        <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span></pre></div>
@@ -1126,7 +1153,7 @@
 <tbody>
 <tr>
   <td>Find the roots of given Quadratic Equation $x^2 + 8x + 8 = 0$</td>
-  <td>$((-1.172, -6.828)) = (\frac{-8 + \sqrt{32}}{2<em>1}, (\frac{-8 - \sqrt{32}}{2</em>1})$</td>
+  <td>$((-1.172, -6.828)) = (\frac{-8 + \sqrt{32}}{2}, (\frac{-8 - \sqrt{32}}{2})$</td>
 </tr>
 </tbody>
 </table>
@@ -1148,7 +1175,7 @@
             <div class="pdoc-code codehilite"><pre><span></span><span id="compound_interest-137"><a href="#compound_interest-137"><span class="linenos">137</span></a><span class="k">def</span> <span class="nf">compound_interest</span><span class="p">(</span><span class="n">max_principle</span><span class="o">=</span><span class="mi">10000</span><span class="p">,</span>
 </span><span id="compound_interest-138"><a href="#compound_interest-138"><span class="linenos">138</span></a>                      <span class="n">max_rate</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
 </span><span id="compound_interest-139"><a href="#compound_interest-139"><span class="linenos">139</span></a>                      <span class="n">max_time</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="compound_interest-140"><a href="#compound_interest-140"><span class="linenos">140</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Compound Interest</span>
+</span><span id="compound_interest-140"><a href="#compound_interest-140"><span class="linenos">140</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Compound Interest</span>
 </span><span id="compound_interest-141"><a href="#compound_interest-141"><span class="linenos">141</span></a>
 </span><span id="compound_interest-142"><a href="#compound_interest-142"><span class="linenos">142</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="compound_interest-143"><a href="#compound_interest-143"><span class="linenos">143</span></a><span class="sd">    | --- | --- |</span>
@@ -1196,7 +1223,7 @@
     </div>
     <a class="headerlink" href="#distance_two_points"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="distance_two_points-155"><a href="#distance_two_points-155"><span class="linenos">155</span></a><span class="k">def</span> <span class="nf">distance_two_points</span><span class="p">(</span><span class="n">max_val_xy</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">min_val_xy</span><span class="o">=-</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="distance_two_points-156"><a href="#distance_two_points-156"><span class="linenos">156</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Distance between 2 points</span>
+</span><span id="distance_two_points-156"><a href="#distance_two_points-156"><span class="linenos">156</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Distance between 2 points</span>
 </span><span id="distance_two_points-157"><a href="#distance_two_points-157"><span class="linenos">157</span></a>
 </span><span id="distance_two_points-158"><a href="#distance_two_points-158"><span class="linenos">158</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="distance_two_points-159"><a href="#distance_two_points-159"><span class="linenos">159</span></a><span class="sd">    | --- | --- |</span>
@@ -1250,7 +1277,7 @@
 </span><span id="expanding-175"><a href="#expanding-175"><span class="linenos">175</span></a>              <span class="n">range_x2</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
 </span><span id="expanding-176"><a href="#expanding-176"><span class="linenos">176</span></a>              <span class="n">range_a</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
 </span><span id="expanding-177"><a href="#expanding-177"><span class="linenos">177</span></a>              <span class="n">range_b</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="expanding-178"><a href="#expanding-178"><span class="linenos">178</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Expanding Factored Binomial</span>
+</span><span id="expanding-178"><a href="#expanding-178"><span class="linenos">178</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Expanding Factored Binomial</span>
 </span><span id="expanding-179"><a href="#expanding-179"><span class="linenos">179</span></a>
 </span><span id="expanding-180"><a href="#expanding-180"><span class="linenos">180</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="expanding-181"><a href="#expanding-181"><span class="linenos">181</span></a><span class="sd">    | --- | --- |</span>
@@ -1332,7 +1359,7 @@
     </div>
     <a class="headerlink" href="#factoring"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="factoring-227"><a href="#factoring-227"><span class="linenos">227</span></a><span class="k">def</span> <span class="nf">factoring</span><span class="p">(</span><span class="n">range_x1</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">range_x2</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="factoring-228"><a href="#factoring-228"><span class="linenos">228</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Factoring Quadratic</span>
+</span><span id="factoring-228"><a href="#factoring-228"><span class="linenos">228</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Factoring Quadratic</span>
 </span><span id="factoring-229"><a href="#factoring-229"><span class="linenos">229</span></a><span class="sd">    Given a quadratic equation in the form x^2 + bx + c, factor it into it&#39;s roots (x - x1)(x -x2)</span>
 </span><span id="factoring-230"><a href="#factoring-230"><span class="linenos">230</span></a>
 </span><span id="factoring-231"><a href="#factoring-231"><span class="linenos">231</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
@@ -1400,7 +1427,7 @@ Given a quadratic equation in the form x^2 + bx + c, factor it into it's roots (
     </div>
     <a class="headerlink" href="#int_matrix_22_determinant"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="int_matrix_22_determinant-262"><a href="#int_matrix_22_determinant-262"><span class="linenos">262</span></a><span class="k">def</span> <span class="nf">int_matrix_22_determinant</span><span class="p">(</span><span class="n">max_matrix_val</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="int_matrix_22_determinant-263"><a href="#int_matrix_22_determinant-263"><span class="linenos">263</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Determinant to 2x2 Matrix</span>
+</span><span id="int_matrix_22_determinant-263"><a href="#int_matrix_22_determinant-263"><span class="linenos">263</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Determinant to 2x2 Matrix</span>
 </span><span id="int_matrix_22_determinant-264"><a href="#int_matrix_22_determinant-264"><span class="linenos">264</span></a>
 </span><span id="int_matrix_22_determinant-265"><a href="#int_matrix_22_determinant-265"><span class="linenos">265</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="int_matrix_22_determinant-266"><a href="#int_matrix_22_determinant-266"><span class="linenos">266</span></a><span class="sd">    | --- | --- |</span>
@@ -1457,14 +1484,14 @@ Given a quadratic equation in the form x^2 + bx + c, factor it into it's roots (
 </span><span id="intersection_of_two_lines-285"><a href="#intersection_of_two_lines-285"><span class="linenos">285</span></a>                              <span class="n">max_b</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
 </span><span id="intersection_of_two_lines-286"><a href="#intersection_of_two_lines-286"><span class="linenos">286</span></a>                              <span class="n">min_denominator</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
 </span><span id="intersection_of_two_lines-287"><a href="#intersection_of_two_lines-287"><span class="linenos">287</span></a>                              <span class="n">max_denominator</span><span class="o">=</span><span class="mi">6</span><span class="p">):</span>
-</span><span id="intersection_of_two_lines-288"><a href="#intersection_of_two_lines-288"><span class="linenos">288</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Intersection of two lines</span>
+</span><span id="intersection_of_two_lines-288"><a href="#intersection_of_two_lines-288"><span class="linenos">288</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Intersection of two lines</span>
 </span><span id="intersection_of_two_lines-289"><a href="#intersection_of_two_lines-289"><span class="linenos">289</span></a>
 </span><span id="intersection_of_two_lines-290"><a href="#intersection_of_two_lines-290"><span class="linenos">290</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="intersection_of_two_lines-291"><a href="#intersection_of_two_lines-291"><span class="linenos">291</span></a><span class="sd">    | --- | --- |</span>
 </span><span id="intersection_of_two_lines-292"><a href="#intersection_of_two_lines-292"><span class="linenos">292</span></a><span class="sd">    | Find the point of intersection of the two lines: $y = \frac{-2}{6}x + 3$ and $y = \frac{3}{6}x - 8$ | $(\frac{66}{5}, \frac{-7}{5})$ |</span>
 </span><span id="intersection_of_two_lines-293"><a href="#intersection_of_two_lines-293"><span class="linenos">293</span></a><span class="sd">    &quot;&quot;&quot;</span>
 </span><span id="intersection_of_two_lines-294"><a href="#intersection_of_two_lines-294"><span class="linenos">294</span></a>    <span class="k">def</span> <span class="nf">generateEquationString</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
-</span><span id="intersection_of_two_lines-295"><a href="#intersection_of_two_lines-295"><span class="linenos">295</span></a>        <span class="sd">&quot;&quot;&quot;</span>
+</span><span id="intersection_of_two_lines-295"><a href="#intersection_of_two_lines-295"><span class="linenos">295</span></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 </span><span id="intersection_of_two_lines-296"><a href="#intersection_of_two_lines-296"><span class="linenos">296</span></a><span class="sd">        Generates an equation given the slope and intercept.</span>
 </span><span id="intersection_of_two_lines-297"><a href="#intersection_of_two_lines-297"><span class="linenos">297</span></a><span class="sd">        It handles cases where m is fractional.</span>
 </span><span id="intersection_of_two_lines-298"><a href="#intersection_of_two_lines-298"><span class="linenos">298</span></a><span class="sd">        It also ensures that we don&#39;t have weird signs such as y = mx + -b.</span>
@@ -1492,9 +1519,9 @@ Given a quadratic equation in the form x^2 + bx + c, factor it into it's roots (
 </span><span id="intersection_of_two_lines-320"><a href="#intersection_of_two_lines-320"><span class="linenos">320</span></a>                <span class="k">return</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2"> + </span><span class="si">{</span><span class="n">b</span><span class="si">}</span><span class="s2">&quot;</span>
 </span><span id="intersection_of_two_lines-321"><a href="#intersection_of_two_lines-321"><span class="linenos">321</span></a>        <span class="k">elif</span> <span class="n">b</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">:</span>
 </span><span id="intersection_of_two_lines-322"><a href="#intersection_of_two_lines-322"><span class="linenos">322</span></a>            <span class="k">if</span> <span class="n">m</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
-</span><span id="intersection_of_two_lines-323"><a href="#intersection_of_two_lines-323"><span class="linenos">323</span></a>                <span class="k">return</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2"> -</span><span class="si">{</span><span class="n">b</span> <span class="o">*</span> <span class="o">-</span><span class="mi">1</span><span class="si">}</span><span class="s2">&quot;</span>
+</span><span id="intersection_of_two_lines-323"><a href="#intersection_of_two_lines-323"><span class="linenos">323</span></a>                <span class="k">return</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2"> -</span><span class="si">{</span><span class="n">b</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="si">}</span><span class="s2">&quot;</span>
 </span><span id="intersection_of_two_lines-324"><a href="#intersection_of_two_lines-324"><span class="linenos">324</span></a>            <span class="k">else</span><span class="p">:</span>
-</span><span id="intersection_of_two_lines-325"><a href="#intersection_of_two_lines-325"><span class="linenos">325</span></a>                <span class="k">return</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2"> - </span><span class="si">{</span><span class="n">b</span> <span class="o">*</span> <span class="o">-</span><span class="mi">1</span><span class="si">}</span><span class="s2">&quot;</span>
+</span><span id="intersection_of_two_lines-325"><a href="#intersection_of_two_lines-325"><span class="linenos">325</span></a>                <span class="k">return</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2"> - </span><span class="si">{</span><span class="n">b</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="si">}</span><span class="s2">&quot;</span>
 </span><span id="intersection_of_two_lines-326"><a href="#intersection_of_two_lines-326"><span class="linenos">326</span></a>        <span class="k">else</span><span class="p">:</span>
 </span><span id="intersection_of_two_lines-327"><a href="#intersection_of_two_lines-327"><span class="linenos">327</span></a>            <span class="k">if</span> <span class="n">m</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
 </span><span id="intersection_of_two_lines-328"><a href="#intersection_of_two_lines-328"><span class="linenos">328</span></a>                <span class="k">return</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2"> 0&quot;</span>
@@ -1502,7 +1529,7 @@ Given a quadratic equation in the form x^2 + bx + c, factor it into it's roots (
 </span><span id="intersection_of_two_lines-330"><a href="#intersection_of_two_lines-330"><span class="linenos">330</span></a>                <span class="k">return</span> <span class="n">base</span>
 </span><span id="intersection_of_two_lines-331"><a href="#intersection_of_two_lines-331"><span class="linenos">331</span></a>
 </span><span id="intersection_of_two_lines-332"><a href="#intersection_of_two_lines-332"><span class="linenos">332</span></a>    <span class="k">def</span> <span class="nf">fractionToString</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
-</span><span id="intersection_of_two_lines-333"><a href="#intersection_of_two_lines-333"><span class="linenos">333</span></a>        <span class="sd">&quot;&quot;&quot;</span>
+</span><span id="intersection_of_two_lines-333"><a href="#intersection_of_two_lines-333"><span class="linenos">333</span></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 </span><span id="intersection_of_two_lines-334"><a href="#intersection_of_two_lines-334"><span class="linenos">334</span></a><span class="sd">        Converts the given fractions.Fraction into a string.</span>
 </span><span id="intersection_of_two_lines-335"><a href="#intersection_of_two_lines-335"><span class="linenos">335</span></a><span class="sd">        &quot;&quot;&quot;</span>
 </span><span id="intersection_of_two_lines-336"><a href="#intersection_of_two_lines-336"><span class="linenos">336</span></a>        <span class="k">if</span> <span class="n">x</span><span class="o">.</span><span class="n">denominator</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
@@ -1576,7 +1603,7 @@ Given a quadratic equation in the form x^2 + bx + c, factor it into it's roots (
             <div class="pdoc-code codehilite"><pre><span></span><span id="invert_matrix-372"><a href="#invert_matrix-372"><span class="linenos">372</span></a><span class="k">def</span> <span class="nf">invert_matrix</span><span class="p">(</span><span class="n">square_matrix_dimension</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span>
 </span><span id="invert_matrix-373"><a href="#invert_matrix-373"><span class="linenos">373</span></a>                  <span class="n">max_matrix_element</span><span class="o">=</span><span class="mi">99</span><span class="p">,</span>
 </span><span id="invert_matrix-374"><a href="#invert_matrix-374"><span class="linenos">374</span></a>                  <span class="n">only_integer_elements_in_inverted_matrixe</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-</span><span id="invert_matrix-375"><a href="#invert_matrix-375"><span class="linenos">375</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Invert Matrix</span>
+</span><span id="invert_matrix-375"><a href="#invert_matrix-375"><span class="linenos">375</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Invert Matrix</span>
 </span><span id="invert_matrix-376"><a href="#invert_matrix-376"><span class="linenos">376</span></a>
 </span><span id="invert_matrix-377"><a href="#invert_matrix-377"><span class="linenos">377</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="invert_matrix-378"><a href="#invert_matrix-378"><span class="linenos">378</span></a><span class="sd">    | --- | --- |</span>
@@ -1689,7 +1716,7 @@ Given a quadratic equation in the form x^2 + bx + c, factor it into it's roots (
     </div>
     <a class="headerlink" href="#linear_equations"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="linear_equations-455"><a href="#linear_equations-455"><span class="linenos">455</span></a><span class="k">def</span> <span class="nf">linear_equations</span><span class="p">(</span><span class="n">n</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">var_range</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">coeff_range</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="linear_equations-456"><a href="#linear_equations-456"><span class="linenos">456</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Linear Equations</span>
+</span><span id="linear_equations-456"><a href="#linear_equations-456"><span class="linenos">456</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Linear Equations</span>
 </span><span id="linear_equations-457"><a href="#linear_equations-457"><span class="linenos">457</span></a>
 </span><span id="linear_equations-458"><a href="#linear_equations-458"><span class="linenos">458</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="linear_equations-459"><a href="#linear_equations-459"><span class="linenos">459</span></a><span class="sd">    | --- | --- |</span>
@@ -1757,7 +1784,7 @@ Given a quadratic equation in the form x^2 + bx + c, factor it into it's roots (
     </div>
     <a class="headerlink" href="#line_equation_from_2_points"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="line_equation_from_2_points-491"><a href="#line_equation_from_2_points-491"><span class="linenos">491</span></a><span class="k">def</span> <span class="nf">line_equation_from_2_points</span><span class="p">(</span><span class="n">max_val</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="line_equation_from_2_points-492"><a href="#line_equation_from_2_points-492"><span class="linenos">492</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Equation of Line from Two Points</span>
+</span><span id="line_equation_from_2_points-492"><a href="#line_equation_from_2_points-492"><span class="linenos">492</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Equation of Line from Two Points</span>
 </span><span id="line_equation_from_2_points-493"><a href="#line_equation_from_2_points-493"><span class="linenos">493</span></a>
 </span><span id="line_equation_from_2_points-494"><a href="#line_equation_from_2_points-494"><span class="linenos">494</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="line_equation_from_2_points-495"><a href="#line_equation_from_2_points-495"><span class="linenos">495</span></a><span class="sd">    | --- | --- |</span>
@@ -1773,11 +1800,11 @@ Given a quadratic equation in the form x^2 + bx + c, factor it into it's roots (
 </span><span id="line_equation_from_2_points-505"><a href="#line_equation_from_2_points-505"><span class="linenos">505</span></a>    <span class="n">m2</span> <span class="o">=</span> <span class="p">(</span><span class="n">x2</span> <span class="o">-</span> <span class="n">x1</span><span class="p">)</span> <span class="o">//</span> <span class="n">math</span><span class="o">.</span><span class="n">gcd</span><span class="p">(</span><span class="n">y2</span> <span class="o">-</span> <span class="n">y1</span><span class="p">,</span> <span class="n">x2</span> <span class="o">-</span> <span class="n">x1</span><span class="p">)</span>
 </span><span id="line_equation_from_2_points-506"><a href="#line_equation_from_2_points-506"><span class="linenos">506</span></a>    <span class="n">c1</span> <span class="o">=</span> <span class="p">(</span><span class="n">y1</span> <span class="o">*</span> <span class="p">(</span><span class="n">x2</span> <span class="o">-</span> <span class="n">x1</span><span class="p">)</span> <span class="o">-</span> <span class="p">(</span><span class="n">y2</span> <span class="o">-</span> <span class="n">y1</span><span class="p">)</span> <span class="o">*</span> <span class="n">x1</span><span class="p">)</span> <span class="o">//</span> <span class="n">math</span><span class="o">.</span><span class="n">gcd</span><span class="p">(</span><span class="n">y1</span> <span class="o">*</span> <span class="p">(</span><span class="n">x2</span> <span class="o">-</span> <span class="n">x1</span><span class="p">)</span> <span class="o">-</span> <span class="p">(</span><span class="n">y2</span> <span class="o">-</span> <span class="n">y1</span><span class="p">)</span> <span class="o">*</span> <span class="n">x1</span><span class="p">,</span> <span class="p">(</span><span class="n">x2</span> <span class="o">-</span> <span class="n">x1</span><span class="p">))</span>
 </span><span id="line_equation_from_2_points-507"><a href="#line_equation_from_2_points-507"><span class="linenos">507</span></a>    <span class="n">c2</span> <span class="o">=</span> <span class="p">(</span><span class="n">x2</span> <span class="o">-</span> <span class="n">x1</span><span class="p">)</span> <span class="o">//</span> <span class="n">math</span><span class="o">.</span><span class="n">gcd</span><span class="p">(</span><span class="n">y1</span> <span class="o">*</span> <span class="p">(</span><span class="n">x2</span> <span class="o">-</span> <span class="n">x1</span><span class="p">)</span> <span class="o">-</span> <span class="p">(</span><span class="n">y2</span> <span class="o">-</span> <span class="n">y1</span><span class="p">)</span> <span class="o">*</span> <span class="n">x1</span><span class="p">,</span> <span class="p">(</span><span class="n">x2</span> <span class="o">-</span> <span class="n">x1</span><span class="p">))</span>
-</span><span id="line_equation_from_2_points-508"><a href="#line_equation_from_2_points-508"><span class="linenos">508</span></a>    <span class="n">c</span> <span class="o">=</span> <span class="sa">rf</span><span class="s2">&quot;</span><span class="si">{</span><span class="s1">&#39;+&#39;</span> <span class="k">if</span> <span class="n">c1</span> <span class="o">&gt;=</span> <span class="mi">0</span> <span class="k">else</span> <span class="s1">&#39;-&#39;</span><span class="si">}</span><span class="s2">\frac</span><span class="se">{{</span><span class="si">{</span><span class="nb">abs</span><span class="p">(</span><span class="n">c1</span><span class="p">)</span><span class="si">}</span><span class="se">}}{{</span><span class="si">{</span><span class="n">c2</span><span class="si">}</span><span class="se">}}</span><span class="s2">&quot;</span> <span class="k">if</span> <span class="n">c1</span> <span class="o">!=</span> <span class="mi">0</span> <span class="k">else</span> <span class="s2">&quot;&quot;</span>
+</span><span id="line_equation_from_2_points-508"><a href="#line_equation_from_2_points-508"><span class="linenos">508</span></a>    <span class="n">c</span> <span class="o">=</span> <span class="sa">rf</span><span class="s2">&quot;</span><span class="si">{</span><span class="s1">&#39;+&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">c1</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="s1">&#39;-&#39;</span><span class="si">}</span><span class="s2">\frac</span><span class="se">{{</span><span class="si">{</span><span class="nb">abs</span><span class="p">(</span><span class="n">c1</span><span class="p">)</span><span class="si">}</span><span class="se">}}{{</span><span class="si">{</span><span class="n">c2</span><span class="si">}</span><span class="se">}}</span><span class="s2">&quot;</span> <span class="k">if</span> <span class="n">c1</span> <span class="o">!=</span> <span class="mi">0</span> <span class="k">else</span> <span class="s2">&quot;&quot;</span>
 </span><span id="line_equation_from_2_points-509"><a href="#line_equation_from_2_points-509"><span class="linenos">509</span></a>    <span class="k">if</span> <span class="n">c2</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">:</span>
 </span><span id="line_equation_from_2_points-510"><a href="#line_equation_from_2_points-510"><span class="linenos">510</span></a>        <span class="n">c2</span> <span class="o">=</span> <span class="o">-</span><span class="n">c2</span>
 </span><span id="line_equation_from_2_points-511"><a href="#line_equation_from_2_points-511"><span class="linenos">511</span></a>        <span class="n">c1</span> <span class="o">=</span> <span class="o">-</span><span class="n">c1</span>
-</span><span id="line_equation_from_2_points-512"><a href="#line_equation_from_2_points-512"><span class="linenos">512</span></a>        <span class="n">c</span> <span class="o">=</span> <span class="sa">rf</span><span class="s2">&quot;</span><span class="si">{</span><span class="s1">&#39;+&#39;</span> <span class="k">if</span> <span class="n">c1</span> <span class="o">&gt;=</span> <span class="mi">0</span> <span class="k">else</span> <span class="s1">&#39;-&#39;</span><span class="si">}</span><span class="s2">\frac</span><span class="se">{{</span><span class="si">{</span><span class="nb">abs</span><span class="p">(</span><span class="n">c1</span><span class="p">)</span><span class="si">}</span><span class="se">}}{{</span><span class="si">{</span><span class="n">c2</span><span class="si">}</span><span class="se">}}</span><span class="s2">&quot;</span>
+</span><span id="line_equation_from_2_points-512"><a href="#line_equation_from_2_points-512"><span class="linenos">512</span></a>        <span class="n">c</span> <span class="o">=</span> <span class="sa">rf</span><span class="s2">&quot;</span><span class="si">{</span><span class="s1">&#39;+&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">c1</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="s1">&#39;-&#39;</span><span class="si">}</span><span class="s2">\frac</span><span class="se">{{</span><span class="si">{</span><span class="nb">abs</span><span class="p">(</span><span class="n">c1</span><span class="p">)</span><span class="si">}</span><span class="se">}}{{</span><span class="si">{</span><span class="n">c2</span><span class="si">}</span><span class="se">}}</span><span class="s2">&quot;</span>
 </span><span id="line_equation_from_2_points-513"><a href="#line_equation_from_2_points-513"><span class="linenos">513</span></a>    <span class="k">if</span> <span class="n">c2</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
 </span><span id="line_equation_from_2_points-514"><a href="#line_equation_from_2_points-514"><span class="linenos">514</span></a>        <span class="n">c</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">c1</span><span class="si">:</span><span class="s2">+</span><span class="si">}</span><span class="s2">&quot;</span>
 </span><span id="line_equation_from_2_points-515"><a href="#line_equation_from_2_points-515"><span class="linenos">515</span></a>
@@ -1831,7 +1858,7 @@ Given a quadratic equation in the form x^2 + bx + c, factor it into it's roots (
     </div>
     <a class="headerlink" href="#log"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="log-533"><a href="#log-533"><span class="linenos">533</span></a><span class="k">def</span> <span class="nf">log</span><span class="p">(</span><span class="n">max_base</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">max_val</span><span class="o">=</span><span class="mi">8</span><span class="p">):</span>
-</span><span id="log-534"><a href="#log-534"><span class="linenos">534</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Logarithm</span>
+</span><span id="log-534"><a href="#log-534"><span class="linenos">534</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Logarithm</span>
 </span><span id="log-535"><a href="#log-535"><span class="linenos">535</span></a>
 </span><span id="log-536"><a href="#log-536"><span class="linenos">536</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="log-537"><a href="#log-537"><span class="linenos">537</span></a><span class="sd">    | --- | --- |</span>
@@ -1879,7 +1906,7 @@ Given a quadratic equation in the form x^2 + bx + c, factor it into it's roots (
     </div>
     <a class="headerlink" href="#matrix_multiplication"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="matrix_multiplication-549"><a href="#matrix_multiplication-549"><span class="linenos">549</span></a><span class="k">def</span> <span class="nf">matrix_multiplication</span><span class="p">(</span><span class="n">max_val</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">max_dim</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="matrix_multiplication-550"><a href="#matrix_multiplication-550"><span class="linenos">550</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Multiply Two Matrices</span>
+</span><span id="matrix_multiplication-550"><a href="#matrix_multiplication-550"><span class="linenos">550</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Multiply Two Matrices</span>
 </span><span id="matrix_multiplication-551"><a href="#matrix_multiplication-551"><span class="linenos">551</span></a>
 </span><span id="matrix_multiplication-552"><a href="#matrix_multiplication-552"><span class="linenos">552</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="matrix_multiplication-553"><a href="#matrix_multiplication-553"><span class="linenos">553</span></a><span class="sd">    | --- | --- |</span>
@@ -1942,7 +1969,7 @@ Given a quadratic equation in the form x^2 + bx + c, factor it into it's roots (
     </div>
     <a class="headerlink" href="#midpoint_of_two_points"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="midpoint_of_two_points-580"><a href="#midpoint_of_two_points-580"><span class="linenos">580</span></a><span class="k">def</span> <span class="nf">midpoint_of_two_points</span><span class="p">(</span><span class="n">max_value</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="midpoint_of_two_points-581"><a href="#midpoint_of_two_points-581"><span class="linenos">581</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Midpoint of two points</span>
+</span><span id="midpoint_of_two_points-581"><a href="#midpoint_of_two_points-581"><span class="linenos">581</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Midpoint of two points</span>
 </span><span id="midpoint_of_two_points-582"><a href="#midpoint_of_two_points-582"><span class="linenos">582</span></a>
 </span><span id="midpoint_of_two_points-583"><a href="#midpoint_of_two_points-583"><span class="linenos">583</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="midpoint_of_two_points-584"><a href="#midpoint_of_two_points-584"><span class="linenos">584</span></a><span class="sd">    | --- | --- |</span>
@@ -1994,7 +2021,7 @@ Given a quadratic equation in the form x^2 + bx + c, factor it into it's roots (
     <a class="headerlink" href="#multiply_complex_numbers"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="multiply_complex_numbers-599"><a href="#multiply_complex_numbers-599"><span class="linenos">599</span></a><span class="k">def</span> <span class="nf">multiply_complex_numbers</span><span class="p">(</span><span class="n">min_real_imaginary_num</span><span class="o">=-</span><span class="mi">20</span><span class="p">,</span>
 </span><span id="multiply_complex_numbers-600"><a href="#multiply_complex_numbers-600"><span class="linenos">600</span></a>                             <span class="n">max_real_imaginary_num</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="multiply_complex_numbers-601"><a href="#multiply_complex_numbers-601"><span class="linenos">601</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Multiplication of 2 complex numbers</span>
+</span><span id="multiply_complex_numbers-601"><a href="#multiply_complex_numbers-601"><span class="linenos">601</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Multiplication of 2 complex numbers</span>
 </span><span id="multiply_complex_numbers-602"><a href="#multiply_complex_numbers-602"><span class="linenos">602</span></a>
 </span><span id="multiply_complex_numbers-603"><a href="#multiply_complex_numbers-603"><span class="linenos">603</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="multiply_complex_numbers-604"><a href="#multiply_complex_numbers-604"><span class="linenos">604</span></a><span class="sd">    | --- | --- |</span>
@@ -2044,7 +2071,7 @@ Given a quadratic equation in the form x^2 + bx + c, factor it into it's roots (
     </div>
     <a class="headerlink" href="#multiply_int_to_22_matrix"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="multiply_int_to_22_matrix-618"><a href="#multiply_int_to_22_matrix-618"><span class="linenos">618</span></a><span class="k">def</span> <span class="nf">multiply_int_to_22_matrix</span><span class="p">(</span><span class="n">max_matrix_val</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">max_res</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="multiply_int_to_22_matrix-619"><a href="#multiply_int_to_22_matrix-619"><span class="linenos">619</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Multiply Integer to 2x2 Matrix</span>
+</span><span id="multiply_int_to_22_matrix-619"><a href="#multiply_int_to_22_matrix-619"><span class="linenos">619</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Multiply Integer to 2x2 Matrix</span>
 </span><span id="multiply_int_to_22_matrix-620"><a href="#multiply_int_to_22_matrix-620"><span class="linenos">620</span></a>
 </span><span id="multiply_int_to_22_matrix-621"><a href="#multiply_int_to_22_matrix-621"><span class="linenos">621</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="multiply_int_to_22_matrix-622"><a href="#multiply_int_to_22_matrix-622"><span class="linenos">622</span></a><span class="sd">    | --- | --- |</span>
@@ -2102,7 +2129,7 @@ Given a quadratic equation in the form x^2 + bx + c, factor it into it's roots (
     </div>
     <a class="headerlink" href="#quadratic_equation"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="quadratic_equation-644"><a href="#quadratic_equation-644"><span class="linenos">644</span></a><span class="k">def</span> <span class="nf">quadratic_equation</span><span class="p">(</span><span class="n">max_val</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="quadratic_equation-645"><a href="#quadratic_equation-645"><span class="linenos">645</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Quadratic Equation</span>
+</span><span id="quadratic_equation-645"><a href="#quadratic_equation-645"><span class="linenos">645</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Quadratic Equation</span>
 </span><span id="quadratic_equation-646"><a href="#quadratic_equation-646"><span class="linenos">646</span></a>
 </span><span id="quadratic_equation-647"><a href="#quadratic_equation-647"><span class="linenos">647</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="quadratic_equation-648"><a href="#quadratic_equation-648"><span class="linenos">648</span></a><span class="sd">    | --- | --- |</span>
@@ -2155,7 +2182,7 @@ Given a quadratic equation in the form x^2 + bx + c, factor it into it's roots (
             <div class="pdoc-code codehilite"><pre><span></span><span id="simple_interest-663"><a href="#simple_interest-663"><span class="linenos">663</span></a><span class="k">def</span> <span class="nf">simple_interest</span><span class="p">(</span><span class="n">max_principle</span><span class="o">=</span><span class="mi">10000</span><span class="p">,</span>
 </span><span id="simple_interest-664"><a href="#simple_interest-664"><span class="linenos">664</span></a>                    <span class="n">max_rate</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
 </span><span id="simple_interest-665"><a href="#simple_interest-665"><span class="linenos">665</span></a>                    <span class="n">max_time</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="simple_interest-666"><a href="#simple_interest-666"><span class="linenos">666</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Simple Interest</span>
+</span><span id="simple_interest-666"><a href="#simple_interest-666"><span class="linenos">666</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Simple Interest</span>
 </span><span id="simple_interest-667"><a href="#simple_interest-667"><span class="linenos">667</span></a>
 </span><span id="simple_interest-668"><a href="#simple_interest-668"><span class="linenos">668</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="simple_interest-669"><a href="#simple_interest-669"><span class="linenos">669</span></a><span class="sd">    | --- | --- |</span>
@@ -2206,7 +2233,7 @@ Given a quadratic equation in the form x^2 + bx + c, factor it into it's roots (
             <div class="pdoc-code codehilite"><pre><span></span><span id="system_of_equations-682"><a href="#system_of_equations-682"><span class="linenos">682</span></a><span class="k">def</span> <span class="nf">system_of_equations</span><span class="p">(</span><span class="n">range_x</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
 </span><span id="system_of_equations-683"><a href="#system_of_equations-683"><span class="linenos">683</span></a>                        <span class="n">range_y</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
 </span><span id="system_of_equations-684"><a href="#system_of_equations-684"><span class="linenos">684</span></a>                        <span class="n">coeff_mult_range</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="system_of_equations-685"><a href="#system_of_equations-685"><span class="linenos">685</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Solve a System of Equations in R^2</span>
+</span><span id="system_of_equations-685"><a href="#system_of_equations-685"><span class="linenos">685</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Solve a System of Equations in R^2</span>
 </span><span id="system_of_equations-686"><a href="#system_of_equations-686"><span class="linenos">686</span></a>
 </span><span id="system_of_equations-687"><a href="#system_of_equations-687"><span class="linenos">687</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="system_of_equations-688"><a href="#system_of_equations-688"><span class="linenos">688</span></a><span class="sd">    | --- | --- |</span>
@@ -2290,7 +2317,7 @@ Given a quadratic equation in the form x^2 + bx + c, factor it into it's roots (
     </div>
     <a class="headerlink" href="#vector_cross"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="vector_cross-736"><a href="#vector_cross-736"><span class="linenos">736</span></a><span class="k">def</span> <span class="nf">vector_cross</span><span class="p">(</span><span class="n">min_val</span><span class="o">=-</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_val</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="vector_cross-737"><a href="#vector_cross-737"><span class="linenos">737</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Cross product of 2 vectors</span>
+</span><span id="vector_cross-737"><a href="#vector_cross-737"><span class="linenos">737</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Cross product of 2 vectors</span>
 </span><span id="vector_cross-738"><a href="#vector_cross-738"><span class="linenos">738</span></a>
 </span><span id="vector_cross-739"><a href="#vector_cross-739"><span class="linenos">739</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="vector_cross-740"><a href="#vector_cross-740"><span class="linenos">740</span></a><span class="sd">    | --- | --- |</span>
@@ -2341,7 +2368,7 @@ Given a quadratic equation in the form x^2 + bx + c, factor it into it's roots (
     </div>
     <a class="headerlink" href="#vector_dot"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="vector_dot-755"><a href="#vector_dot-755"><span class="linenos">755</span></a><span class="k">def</span> <span class="nf">vector_dot</span><span class="p">(</span><span class="n">min_val</span><span class="o">=-</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_val</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="vector_dot-756"><a href="#vector_dot-756"><span class="linenos">756</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Dot product of 2 vectors</span>
+</span><span id="vector_dot-756"><a href="#vector_dot-756"><span class="linenos">756</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Dot product of 2 vectors</span>
 </span><span id="vector_dot-757"><a href="#vector_dot-757"><span class="linenos">757</span></a>
 </span><span id="vector_dot-758"><a href="#vector_dot-758"><span class="linenos">758</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="vector_dot-759"><a href="#vector_dot-759"><span class="linenos">759</span></a><span class="sd">    | --- | --- |</span>
@@ -2376,6 +2403,62 @@ Given a quadratic equation in the form x^2 + bx + c, factor it into it's roots (
 </div>
 
 
+                </section>
+                <section id="orthogonal_projection">
+                            <input id="orthogonal_projection-view-source" class="view-source-toggle-state" type="checkbox" aria-hidden="true" tabindex="-1">
+<div class="attr function">
+            
+        <span class="def">def</span>
+        <span class="name">orthogonal_projection</span><span class="signature pdoc-code condensed">(<span class="param"><span class="n">min_val</span><span class="o">=-</span><span class="mi">10</span>, </span><span class="param"><span class="n">max_val</span><span class="o">=</span><span class="mi">10</span></span><span class="return-annotation">):</span></span>
+
+                <label class="view-source-button" for="orthogonal_projection-view-source"><span>View Source</span></label>
+
+    </div>
+    <a class="headerlink" href="#orthogonal_projection"></a>
+            <div class="pdoc-code codehilite"><pre><span></span><span id="orthogonal_projection-771"><a href="#orthogonal_projection-771"><span class="linenos">771</span></a><span class="k">def</span> <span class="nf">orthogonal_projection</span><span class="p">(</span><span class="n">min_val</span><span class="o">=-</span><span class="mi">10</span><span class="p">,</span> <span class="n">max_val</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
+</span><span id="orthogonal_projection-772"><a href="#orthogonal_projection-772"><span class="linenos">772</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Orthogonal Projection</span>
+</span><span id="orthogonal_projection-773"><a href="#orthogonal_projection-773"><span class="linenos">773</span></a>
+</span><span id="orthogonal_projection-774"><a href="#orthogonal_projection-774"><span class="linenos">774</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
+</span><span id="orthogonal_projection-775"><a href="#orthogonal_projection-775"><span class="linenos">775</span></a><span class="sd">    | --- | --- |</span>
+</span><span id="orthogonal_projection-776"><a href="#orthogonal_projection-776"><span class="linenos">776</span></a><span class="sd">    | Find the orthogonal projection of $[2, 3]$ onto $[4, -7]$ | $[\frac{-4}{5}, \frac{7}{5}]$ |</span>
+</span><span id="orthogonal_projection-777"><a href="#orthogonal_projection-777"><span class="linenos">777</span></a><span class="sd">    &quot;&quot;&quot;</span>
+</span><span id="orthogonal_projection-778"><a href="#orthogonal_projection-778"><span class="linenos">778</span></a>    <span class="n">v</span> <span class="o">=</span> <span class="p">[</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="n">min_val</span><span class="p">,</span> <span class="n">max_val</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">)]</span>
+</span><span id="orthogonal_projection-779"><a href="#orthogonal_projection-779"><span class="linenos">779</span></a>    <span class="n">u</span> <span class="o">=</span> <span class="p">[</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="n">min_val</span><span class="p">,</span> <span class="n">max_val</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">)]</span>
+</span><span id="orthogonal_projection-780"><a href="#orthogonal_projection-780"><span class="linenos">780</span></a>    <span class="n">dot_t</span> <span class="o">=</span> <span class="n">v</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">u</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">u</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+</span><span id="orthogonal_projection-781"><a href="#orthogonal_projection-781"><span class="linenos">781</span></a>    <span class="n">dot_b</span> <span class="o">=</span> <span class="n">u</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">u</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">u</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">u</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+</span><span id="orthogonal_projection-782"><a href="#orthogonal_projection-782"><span class="linenos">782</span></a>    <span class="n">frac</span> <span class="o">=</span> <span class="n">fractions</span><span class="o">.</span><span class="n">Fraction</span><span class="p">(</span><span class="n">dot_t</span><span class="p">,</span> <span class="n">dot_b</span><span class="p">)</span><span class="o">.</span><span class="n">limit_denominator</span><span class="p">()</span>
+</span><span id="orthogonal_projection-783"><a href="#orthogonal_projection-783"><span class="linenos">783</span></a>    <span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="n">frac</span> <span class="o">*</span> <span class="n">u</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">frac</span> <span class="o">*</span> <span class="n">u</span><span class="p">[</span><span class="mi">1</span><span class="p">]]</span>
+</span><span id="orthogonal_projection-784"><a href="#orthogonal_projection-784"><span class="linenos">784</span></a>
+</span><span id="orthogonal_projection-785"><a href="#orthogonal_projection-785"><span class="linenos">785</span></a>    <span class="k">if</span> <span class="n">y</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">denominator</span> <span class="o">!=</span> <span class="mi">1</span><span class="p">:</span>
+</span><span id="orthogonal_projection-786"><a href="#orthogonal_projection-786"><span class="linenos">786</span></a>        <span class="n">y</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;\frac</span><span class="se">{{</span><span class="si">{</span><span class="n">y</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">numerator</span><span class="si">}</span><span class="se">}}{{</span><span class="si">{</span><span class="n">y</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">denominator</span><span class="si">}</span><span class="se">}}</span><span class="s1">&#39;</span>
+</span><span id="orthogonal_projection-787"><a href="#orthogonal_projection-787"><span class="linenos">787</span></a>    <span class="k">if</span> <span class="n">y</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">denominator</span> <span class="o">!=</span> <span class="mi">1</span><span class="p">:</span>
+</span><span id="orthogonal_projection-788"><a href="#orthogonal_projection-788"><span class="linenos">788</span></a>        <span class="n">y</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;\frac</span><span class="se">{{</span><span class="si">{</span><span class="n">y</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">numerator</span><span class="si">}</span><span class="se">}}{{</span><span class="si">{</span><span class="n">y</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">denominator</span><span class="si">}</span><span class="se">}}</span><span class="s1">&#39;</span>
+</span><span id="orthogonal_projection-789"><a href="#orthogonal_projection-789"><span class="linenos">789</span></a>
+</span><span id="orthogonal_projection-790"><a href="#orthogonal_projection-790"><span class="linenos">790</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;Find the orthogonal projection of $</span><span class="si">{</span><span class="n">v</span><span class="si">}</span><span class="s1">$ onto $</span><span class="si">{</span><span class="n">u</span><span class="si">}</span><span class="s1">$&#39;</span>
+</span><span id="orthogonal_projection-791"><a href="#orthogonal_projection-791"><span class="linenos">791</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$[</span><span class="si">{</span><span class="n">y</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="si">}</span><span class="s1">, </span><span class="si">{</span><span class="n">y</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="si">}</span><span class="s1">]$&#39;</span>
+</span><span id="orthogonal_projection-792"><a href="#orthogonal_projection-792"><span class="linenos">792</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
+</span></pre></div>
+
+
+            <div class="docstring"><p>Orthogonal Projection</p>
+
+<table>
+<thead>
+<tr>
+  <th>Ex. Problem</th>
+  <th>Ex. Solution</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+  <td>Find the orthogonal projection of $[2, 3]$ onto $[4, -7]$</td>
+  <td>$[\frac{-4}{5}, \frac{7}{5}]$</td>
+</tr>
+</tbody>
+</table>
+</div>
+
+
                 </section>
     </main>
 <script>
@@ -2497,7 +2580,7 @@ Given a quadratic equation in the form x^2 + bx + c, factor it into it's roots (
                         if (doc.annotation)
                             heading += `<span class="annotation">${doc.annotation}</span>`;
                         if (doc.default_value)
-                            heading += `<span class="default_value">${doc.default_value}</span>`;
+                            heading += `<span class="default_value"> = ${doc.default_value}</span>`;
                         break;
                     default:
                         heading = `<span class="name">${doc.fullname}</span>`;
diff --git a/docs/mathgenerator/basic_math.html b/docs/mathgenerator/basic_math.html
index 290a6db..3552ee0 100644
--- a/docs/mathgenerator/basic_math.html
+++ b/docs/mathgenerator/basic_math.html
@@ -3,14 +3,14 @@
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     <title>mathgenerator.basic_math API documentation</title>
 
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@@ -50,8 +50,8 @@
 
 
 
-        <h2>API Documentation</h2>
-            <ul class="memberlist">
+            <h2>API Documentation</h2>
+                <ul class="memberlist">
             <li>
                     <a class="function" href="#absolute_difference">absolute_difference</a>
             </li>
@@ -143,11 +143,11 @@
 </span><span id="L-2"><a href="#L-2"><span class="linenos">  2</span></a>
 </span><span id="L-3"><a href="#L-3"><span class="linenos">  3</span></a>
 </span><span id="L-4"><a href="#L-4"><span class="linenos">  4</span></a><span class="k">def</span> <span class="nf">absolute_difference</span><span class="p">(</span><span class="n">max_a</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">max_b</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="L-5"><a href="#L-5"><span class="linenos">  5</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Absolute difference between two numbers</span>
+</span><span id="L-5"><a href="#L-5"><span class="linenos">  5</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Absolute difference between two numbers</span>
 </span><span id="L-6"><a href="#L-6"><span class="linenos">  6</span></a>
 </span><span id="L-7"><a href="#L-7"><span class="linenos">  7</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-8"><a href="#L-8"><span class="linenos">  8</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="L-9"><a href="#L-9"><span class="linenos">  9</span></a><span class="sd">    | $|22-34|=$ | $12$ |</span>
+</span><span id="L-9"><a href="#L-9"><span class="linenos">  9</span></a><span class="sd">    | $\|22-34\|=$ | $12$ |</span>
 </span><span id="L-10"><a href="#L-10"><span class="linenos"> 10</span></a><span class="sd">    &quot;&quot;&quot;</span>
 </span><span id="L-11"><a href="#L-11"><span class="linenos"> 11</span></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">max_a</span><span class="p">,</span> <span class="n">max_a</span><span class="p">)</span>
 </span><span id="L-12"><a href="#L-12"><span class="linenos"> 12</span></a>    <span class="n">b</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">max_b</span><span class="p">,</span> <span class="n">max_b</span><span class="p">)</span>
@@ -157,7 +157,7 @@
 </span><span id="L-16"><a href="#L-16"><span class="linenos"> 16</span></a>
 </span><span id="L-17"><a href="#L-17"><span class="linenos"> 17</span></a>
 </span><span id="L-18"><a href="#L-18"><span class="linenos"> 18</span></a><span class="k">def</span> <span class="nf">addition</span><span class="p">(</span><span class="n">max_sum</span><span class="o">=</span><span class="mi">99</span><span class="p">,</span> <span class="n">max_addend</span><span class="o">=</span><span class="mi">50</span><span class="p">):</span>
-</span><span id="L-19"><a href="#L-19"><span class="linenos"> 19</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Addition of two numbers</span>
+</span><span id="L-19"><a href="#L-19"><span class="linenos"> 19</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Addition of two numbers</span>
 </span><span id="L-20"><a href="#L-20"><span class="linenos"> 20</span></a>
 </span><span id="L-21"><a href="#L-21"><span class="linenos"> 21</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-22"><a href="#L-22"><span class="linenos"> 22</span></a><span class="sd">    | --- | --- |</span>
@@ -176,7 +176,7 @@
 </span><span id="L-35"><a href="#L-35"><span class="linenos"> 35</span></a>
 </span><span id="L-36"><a href="#L-36"><span class="linenos"> 36</span></a>
 </span><span id="L-37"><a href="#L-37"><span class="linenos"> 37</span></a><span class="k">def</span> <span class="nf">compare_fractions</span><span class="p">(</span><span class="n">max_val</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-38"><a href="#L-38"><span class="linenos"> 38</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Compare Fractions</span>
+</span><span id="L-38"><a href="#L-38"><span class="linenos"> 38</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Compare Fractions</span>
 </span><span id="L-39"><a href="#L-39"><span class="linenos"> 39</span></a>
 </span><span id="L-40"><a href="#L-40"><span class="linenos"> 40</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-41"><a href="#L-41"><span class="linenos"> 41</span></a><span class="sd">    | --- | --- |</span>
@@ -207,7 +207,7 @@
 </span><span id="L-66"><a href="#L-66"><span class="linenos"> 66</span></a>
 </span><span id="L-67"><a href="#L-67"><span class="linenos"> 67</span></a>
 </span><span id="L-68"><a href="#L-68"><span class="linenos"> 68</span></a><span class="k">def</span> <span class="nf">cube_root</span><span class="p">(</span><span class="n">min_no</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_no</span><span class="o">=</span><span class="mi">1000</span><span class="p">):</span>
-</span><span id="L-69"><a href="#L-69"><span class="linenos"> 69</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Cube Root</span>
+</span><span id="L-69"><a href="#L-69"><span class="linenos"> 69</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Cube Root</span>
 </span><span id="L-70"><a href="#L-70"><span class="linenos"> 70</span></a>
 </span><span id="L-71"><a href="#L-71"><span class="linenos"> 71</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-72"><a href="#L-72"><span class="linenos"> 72</span></a><span class="sd">    | --- | --- |</span>
@@ -216,11 +216,11 @@
 </span><span id="L-75"><a href="#L-75"><span class="linenos"> 75</span></a>    <span class="n">b</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="n">min_no</span><span class="p">,</span> <span class="n">max_no</span><span class="p">)</span>
 </span><span id="L-76"><a href="#L-76"><span class="linenos"> 76</span></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">b</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">3</span><span class="p">)</span>
 </span><span id="L-77"><a href="#L-77"><span class="linenos"> 77</span></a>
-</span><span id="L-78"><a href="#L-78"><span class="linenos"> 78</span></a>    <span class="k">return</span> <span class="p">(</span><span class="sa">rf</span><span class="s2">&quot;What is the cube root of: $\sqrt[3]</span><span class="se">{{</span><span class="si">{</span><span class="n">b</span><span class="si">}</span><span class="se">}}</span><span class="s2">=$ to 2 decimal places?&quot;</span><span class="p">,</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="nb">round</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span><span class="si">}</span><span class="s2">$&quot;</span><span class="p">)</span>
+</span><span id="L-78"><a href="#L-78"><span class="linenos"> 78</span></a>    <span class="k">return</span> <span class="p">(</span><span class="sa">rf</span><span class="s2">&quot;What is the cube root of: $\sqrt[3]</span><span class="se">{{</span><span class="si">{</span><span class="n">b</span><span class="si">}</span><span class="se">}}</span><span class="s2">=$ to 2 decimal places?&quot;</span><span class="p">,</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="nb">round</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="si">}</span><span class="s2">$&quot;</span><span class="p">)</span>
 </span><span id="L-79"><a href="#L-79"><span class="linenos"> 79</span></a>
 </span><span id="L-80"><a href="#L-80"><span class="linenos"> 80</span></a>
 </span><span id="L-81"><a href="#L-81"><span class="linenos"> 81</span></a><span class="k">def</span> <span class="nf">divide_fractions</span><span class="p">(</span><span class="n">max_val</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-82"><a href="#L-82"><span class="linenos"> 82</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Divide Fractions</span>
+</span><span id="L-82"><a href="#L-82"><span class="linenos"> 82</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Divide Fractions</span>
 </span><span id="L-83"><a href="#L-83"><span class="linenos"> 83</span></a>
 </span><span id="L-84"><a href="#L-84"><span class="linenos"> 84</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-85"><a href="#L-85"><span class="linenos"> 85</span></a><span class="sd">    | --- | --- |</span>
@@ -253,7 +253,7 @@
 </span><span id="L-112"><a href="#L-112"><span class="linenos">112</span></a>
 </span><span id="L-113"><a href="#L-113"><span class="linenos">113</span></a>
 </span><span id="L-114"><a href="#L-114"><span class="linenos">114</span></a><span class="k">def</span> <span class="nf">division</span><span class="p">(</span><span class="n">max_a</span><span class="o">=</span><span class="mi">25</span><span class="p">,</span> <span class="n">max_b</span><span class="o">=</span><span class="mi">25</span><span class="p">):</span>
-</span><span id="L-115"><a href="#L-115"><span class="linenos">115</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Division</span>
+</span><span id="L-115"><a href="#L-115"><span class="linenos">115</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Division</span>
 </span><span id="L-116"><a href="#L-116"><span class="linenos">116</span></a>
 </span><span id="L-117"><a href="#L-117"><span class="linenos">117</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-118"><a href="#L-118"><span class="linenos">118</span></a><span class="sd">    | --- | --- |</span>
@@ -270,7 +270,7 @@
 </span><span id="L-129"><a href="#L-129"><span class="linenos">129</span></a>
 </span><span id="L-130"><a href="#L-130"><span class="linenos">130</span></a>
 </span><span id="L-131"><a href="#L-131"><span class="linenos">131</span></a><span class="k">def</span> <span class="nf">exponentiation</span><span class="p">(</span><span class="n">max_base</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_expo</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-132"><a href="#L-132"><span class="linenos">132</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Exponentiation</span>
+</span><span id="L-132"><a href="#L-132"><span class="linenos">132</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Exponentiation</span>
 </span><span id="L-133"><a href="#L-133"><span class="linenos">133</span></a>
 </span><span id="L-134"><a href="#L-134"><span class="linenos">134</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-135"><a href="#L-135"><span class="linenos">135</span></a><span class="sd">    | --- | --- |</span>
@@ -283,7 +283,7 @@
 </span><span id="L-142"><a href="#L-142"><span class="linenos">142</span></a>
 </span><span id="L-143"><a href="#L-143"><span class="linenos">143</span></a>
 </span><span id="L-144"><a href="#L-144"><span class="linenos">144</span></a><span class="k">def</span> <span class="nf">factorial</span><span class="p">(</span><span class="n">max_input</span><span class="o">=</span><span class="mi">6</span><span class="p">):</span>
-</span><span id="L-145"><a href="#L-145"><span class="linenos">145</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Factorial</span>
+</span><span id="L-145"><a href="#L-145"><span class="linenos">145</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Factorial</span>
 </span><span id="L-146"><a href="#L-146"><span class="linenos">146</span></a>
 </span><span id="L-147"><a href="#L-147"><span class="linenos">147</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-148"><a href="#L-148"><span class="linenos">148</span></a><span class="sd">    | --- | --- |</span>
@@ -300,7 +300,7 @@
 </span><span id="L-159"><a href="#L-159"><span class="linenos">159</span></a>
 </span><span id="L-160"><a href="#L-160"><span class="linenos">160</span></a>
 </span><span id="L-161"><a href="#L-161"><span class="linenos">161</span></a><span class="k">def</span> <span class="nf">fraction_multiplication</span><span class="p">(</span><span class="n">max_val</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-162"><a href="#L-162"><span class="linenos">162</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Fraction Multiplication</span>
+</span><span id="L-162"><a href="#L-162"><span class="linenos">162</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Fraction Multiplication</span>
 </span><span id="L-163"><a href="#L-163"><span class="linenos">163</span></a>
 </span><span id="L-164"><a href="#L-164"><span class="linenos">164</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-165"><a href="#L-165"><span class="linenos">165</span></a><span class="sd">    | --- | --- |</span>
@@ -336,7 +336,7 @@
 </span><span id="L-195"><a href="#L-195"><span class="linenos">195</span></a>
 </span><span id="L-196"><a href="#L-196"><span class="linenos">196</span></a>
 </span><span id="L-197"><a href="#L-197"><span class="linenos">197</span></a><span class="k">def</span> <span class="nf">fraction_to_decimal</span><span class="p">(</span><span class="n">max_res</span><span class="o">=</span><span class="mi">99</span><span class="p">,</span> <span class="n">max_divid</span><span class="o">=</span><span class="mi">99</span><span class="p">):</span>
-</span><span id="L-198"><a href="#L-198"><span class="linenos">198</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Fraction to Decimal</span>
+</span><span id="L-198"><a href="#L-198"><span class="linenos">198</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Fraction to Decimal</span>
 </span><span id="L-199"><a href="#L-199"><span class="linenos">199</span></a>
 </span><span id="L-200"><a href="#L-200"><span class="linenos">200</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-201"><a href="#L-201"><span class="linenos">201</span></a><span class="sd">    | --- | --- |</span>
@@ -350,7 +350,7 @@
 </span><span id="L-209"><a href="#L-209"><span class="linenos">209</span></a>
 </span><span id="L-210"><a href="#L-210"><span class="linenos">210</span></a>
 </span><span id="L-211"><a href="#L-211"><span class="linenos">211</span></a><span class="k">def</span> <span class="nf">greatest_common_divisor</span><span class="p">(</span><span class="n">numbers_count</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">max_num</span><span class="o">=</span><span class="mi">10</span><span class="o">**</span><span class="mi">3</span><span class="p">):</span>
-</span><span id="L-212"><a href="#L-212"><span class="linenos">212</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Greatest Common Divisor of N Numbers ( GCD / HCF )</span>
+</span><span id="L-212"><a href="#L-212"><span class="linenos">212</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Greatest Common Divisor of N Numbers ( GCD / HCF )</span>
 </span><span id="L-213"><a href="#L-213"><span class="linenos">213</span></a>
 </span><span id="L-214"><a href="#L-214"><span class="linenos">214</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-215"><a href="#L-215"><span class="linenos">215</span></a><span class="sd">    | --- | --- |</span>
@@ -375,11 +375,11 @@
 </span><span id="L-234"><a href="#L-234"><span class="linenos">234</span></a>        <span class="n">greatestCommonDivisor</span> <span class="o">=</span> <span class="n">greatestCommonDivisorOfTwoNumbers</span><span class="p">(</span>
 </span><span id="L-235"><a href="#L-235"><span class="linenos">235</span></a>            <span class="n">numbers</span><span class="p">[</span><span class="n">index</span><span class="p">],</span> <span class="n">greatestCommonDivisor</span><span class="p">)</span>
 </span><span id="L-236"><a href="#L-236"><span class="linenos">236</span></a>
-</span><span id="L-237"><a href="#L-237"><span class="linenos">237</span></a>    <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;$GCD(</span><span class="si">{</span><span class="s2">&quot;,&quot;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="n">numbers</span><span class="p">))</span><span class="si">}</span><span class="s1">)=$&#39;</span><span class="p">,</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">greatestCommonDivisor</span><span class="si">}</span><span class="s2">$&quot;</span>
+</span><span id="L-237"><a href="#L-237"><span class="linenos">237</span></a>    <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;$GCD(</span><span class="si">{</span><span class="s2">&quot;,&quot;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span><span class="w"> </span><span class="n">numbers</span><span class="p">))</span><span class="si">}</span><span class="s1">)=$&#39;</span><span class="p">,</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">greatestCommonDivisor</span><span class="si">}</span><span class="s2">$&quot;</span>
 </span><span id="L-238"><a href="#L-238"><span class="linenos">238</span></a>
 </span><span id="L-239"><a href="#L-239"><span class="linenos">239</span></a>
 </span><span id="L-240"><a href="#L-240"><span class="linenos">240</span></a><span class="k">def</span> <span class="nf">is_composite</span><span class="p">(</span><span class="n">max_num</span><span class="o">=</span><span class="mi">250</span><span class="p">):</span>
-</span><span id="L-241"><a href="#L-241"><span class="linenos">241</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Is Composite</span>
+</span><span id="L-241"><a href="#L-241"><span class="linenos">241</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Is Composite</span>
 </span><span id="L-242"><a href="#L-242"><span class="linenos">242</span></a>
 </span><span id="L-243"><a href="#L-243"><span class="linenos">243</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-244"><a href="#L-244"><span class="linenos">244</span></a><span class="sd">    | --- | --- |</span>
@@ -399,7 +399,7 @@
 </span><span id="L-258"><a href="#L-258"><span class="linenos">258</span></a>
 </span><span id="L-259"><a href="#L-259"><span class="linenos">259</span></a>
 </span><span id="L-260"><a href="#L-260"><span class="linenos">260</span></a><span class="k">def</span> <span class="nf">is_prime</span><span class="p">(</span><span class="n">max_num</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="L-261"><a href="#L-261"><span class="linenos">261</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Is Prime</span>
+</span><span id="L-261"><a href="#L-261"><span class="linenos">261</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Is Prime</span>
 </span><span id="L-262"><a href="#L-262"><span class="linenos">262</span></a>
 </span><span id="L-263"><a href="#L-263"><span class="linenos">263</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-264"><a href="#L-264"><span class="linenos">264</span></a><span class="sd">    | --- | --- |</span>
@@ -420,7 +420,7 @@
 </span><span id="L-279"><a href="#L-279"><span class="linenos">279</span></a>
 </span><span id="L-280"><a href="#L-280"><span class="linenos">280</span></a>
 </span><span id="L-281"><a href="#L-281"><span class="linenos">281</span></a><span class="k">def</span> <span class="nf">multiplication</span><span class="p">(</span><span class="n">max_multi</span><span class="o">=</span><span class="mi">12</span><span class="p">):</span>
-</span><span id="L-282"><a href="#L-282"><span class="linenos">282</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Multiplication</span>
+</span><span id="L-282"><a href="#L-282"><span class="linenos">282</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Multiplication</span>
 </span><span id="L-283"><a href="#L-283"><span class="linenos">283</span></a>
 </span><span id="L-284"><a href="#L-284"><span class="linenos">284</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-285"><a href="#L-285"><span class="linenos">285</span></a><span class="sd">    | --- | --- |</span>
@@ -434,7 +434,7 @@
 </span><span id="L-293"><a href="#L-293"><span class="linenos">293</span></a>
 </span><span id="L-294"><a href="#L-294"><span class="linenos">294</span></a>
 </span><span id="L-295"><a href="#L-295"><span class="linenos">295</span></a><span class="k">def</span> <span class="nf">percentage</span><span class="p">(</span><span class="n">max_value</span><span class="o">=</span><span class="mi">99</span><span class="p">,</span> <span class="n">max_percentage</span><span class="o">=</span><span class="mi">99</span><span class="p">):</span>
-</span><span id="L-296"><a href="#L-296"><span class="linenos">296</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Percentage of a number</span>
+</span><span id="L-296"><a href="#L-296"><span class="linenos">296</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Percentage of a number</span>
 </span><span id="L-297"><a href="#L-297"><span class="linenos">297</span></a>
 </span><span id="L-298"><a href="#L-298"><span class="linenos">298</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-299"><a href="#L-299"><span class="linenos">299</span></a><span class="sd">    | --- | --- |</span>
@@ -451,7 +451,7 @@
 </span><span id="L-310"><a href="#L-310"><span class="linenos">310</span></a>
 </span><span id="L-311"><a href="#L-311"><span class="linenos">311</span></a>
 </span><span id="L-312"><a href="#L-312"><span class="linenos">312</span></a><span class="k">def</span> <span class="nf">percentage_difference</span><span class="p">(</span><span class="n">max_value</span><span class="o">=</span><span class="mi">200</span><span class="p">,</span> <span class="n">min_value</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
-</span><span id="L-313"><a href="#L-313"><span class="linenos">313</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Percentage difference between two numbers</span>
+</span><span id="L-313"><a href="#L-313"><span class="linenos">313</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Percentage difference between two numbers</span>
 </span><span id="L-314"><a href="#L-314"><span class="linenos">314</span></a>
 </span><span id="L-315"><a href="#L-315"><span class="linenos">315</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-316"><a href="#L-316"><span class="linenos">316</span></a><span class="sd">    | --- | --- |</span>
@@ -469,7 +469,7 @@
 </span><span id="L-328"><a href="#L-328"><span class="linenos">328</span></a>
 </span><span id="L-329"><a href="#L-329"><span class="linenos">329</span></a>
 </span><span id="L-330"><a href="#L-330"><span class="linenos">330</span></a><span class="k">def</span> <span class="nf">percentage_error</span><span class="p">(</span><span class="n">max_value</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">min_value</span><span class="o">=-</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="L-331"><a href="#L-331"><span class="linenos">331</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Percentage error</span>
+</span><span id="L-331"><a href="#L-331"><span class="linenos">331</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Percentage error</span>
 </span><span id="L-332"><a href="#L-332"><span class="linenos">332</span></a>
 </span><span id="L-333"><a href="#L-333"><span class="linenos">333</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-334"><a href="#L-334"><span class="linenos">334</span></a><span class="sd">    | --- | --- |</span>
@@ -490,7 +490,7 @@
 </span><span id="L-349"><a href="#L-349"><span class="linenos">349</span></a>
 </span><span id="L-350"><a href="#L-350"><span class="linenos">350</span></a>
 </span><span id="L-351"><a href="#L-351"><span class="linenos">351</span></a><span class="k">def</span> <span class="nf">power_of_powers</span><span class="p">(</span><span class="n">max_base</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">max_power</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-352"><a href="#L-352"><span class="linenos">352</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Power of Powers</span>
+</span><span id="L-352"><a href="#L-352"><span class="linenos">352</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Power of Powers</span>
 </span><span id="L-353"><a href="#L-353"><span class="linenos">353</span></a>
 </span><span id="L-354"><a href="#L-354"><span class="linenos">354</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-355"><a href="#L-355"><span class="linenos">355</span></a><span class="sd">    | --- | --- |</span>
@@ -507,7 +507,7 @@
 </span><span id="L-366"><a href="#L-366"><span class="linenos">366</span></a>
 </span><span id="L-367"><a href="#L-367"><span class="linenos">367</span></a>
 </span><span id="L-368"><a href="#L-368"><span class="linenos">368</span></a><span class="k">def</span> <span class="nf">square</span><span class="p">(</span><span class="n">max_square_num</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="L-369"><a href="#L-369"><span class="linenos">369</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Square</span>
+</span><span id="L-369"><a href="#L-369"><span class="linenos">369</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Square</span>
 </span><span id="L-370"><a href="#L-370"><span class="linenos">370</span></a>
 </span><span id="L-371"><a href="#L-371"><span class="linenos">371</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-372"><a href="#L-372"><span class="linenos">372</span></a><span class="sd">    | --- | --- |</span>
@@ -520,7 +520,7 @@
 </span><span id="L-379"><a href="#L-379"><span class="linenos">379</span></a>
 </span><span id="L-380"><a href="#L-380"><span class="linenos">380</span></a>
 </span><span id="L-381"><a href="#L-381"><span class="linenos">381</span></a><span class="k">def</span> <span class="nf">square_root</span><span class="p">(</span><span class="n">min_no</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_no</span><span class="o">=</span><span class="mi">12</span><span class="p">):</span>
-</span><span id="L-382"><a href="#L-382"><span class="linenos">382</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Square Root</span>
+</span><span id="L-382"><a href="#L-382"><span class="linenos">382</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Square Root</span>
 </span><span id="L-383"><a href="#L-383"><span class="linenos">383</span></a>
 </span><span id="L-384"><a href="#L-384"><span class="linenos">384</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-385"><a href="#L-385"><span class="linenos">385</span></a><span class="sd">    | --- | --- |</span>
@@ -533,7 +533,7 @@
 </span><span id="L-392"><a href="#L-392"><span class="linenos">392</span></a>
 </span><span id="L-393"><a href="#L-393"><span class="linenos">393</span></a>
 </span><span id="L-394"><a href="#L-394"><span class="linenos">394</span></a><span class="k">def</span> <span class="nf">simplify_square_root</span><span class="p">(</span><span class="n">max_variable</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="L-395"><a href="#L-395"><span class="linenos">395</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Simplify Square Root</span>
+</span><span id="L-395"><a href="#L-395"><span class="linenos">395</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Simplify Square Root</span>
 </span><span id="L-396"><a href="#L-396"><span class="linenos">396</span></a>
 </span><span id="L-397"><a href="#L-397"><span class="linenos">397</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-398"><a href="#L-398"><span class="linenos">398</span></a><span class="sd">    | --- | --- |</span>
@@ -564,7 +564,7 @@
 </span><span id="L-423"><a href="#L-423"><span class="linenos">423</span></a>
 </span><span id="L-424"><a href="#L-424"><span class="linenos">424</span></a>
 </span><span id="L-425"><a href="#L-425"><span class="linenos">425</span></a><span class="k">def</span> <span class="nf">subtraction</span><span class="p">(</span><span class="n">max_minuend</span><span class="o">=</span><span class="mi">99</span><span class="p">,</span> <span class="n">max_diff</span><span class="o">=</span><span class="mi">99</span><span class="p">):</span>
-</span><span id="L-426"><a href="#L-426"><span class="linenos">426</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Subtraction of two numbers</span>
+</span><span id="L-426"><a href="#L-426"><span class="linenos">426</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Subtraction of two numbers</span>
 </span><span id="L-427"><a href="#L-427"><span class="linenos">427</span></a>
 </span><span id="L-428"><a href="#L-428"><span class="linenos">428</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-429"><a href="#L-429"><span class="linenos">429</span></a><span class="sd">    | --- | --- |</span>
@@ -591,11 +591,11 @@
     </div>
     <a class="headerlink" href="#absolute_difference"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="absolute_difference-5"><a href="#absolute_difference-5"><span class="linenos"> 5</span></a><span class="k">def</span> <span class="nf">absolute_difference</span><span class="p">(</span><span class="n">max_a</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">max_b</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="absolute_difference-6"><a href="#absolute_difference-6"><span class="linenos"> 6</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Absolute difference between two numbers</span>
+</span><span id="absolute_difference-6"><a href="#absolute_difference-6"><span class="linenos"> 6</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Absolute difference between two numbers</span>
 </span><span id="absolute_difference-7"><a href="#absolute_difference-7"><span class="linenos"> 7</span></a>
 </span><span id="absolute_difference-8"><a href="#absolute_difference-8"><span class="linenos"> 8</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="absolute_difference-9"><a href="#absolute_difference-9"><span class="linenos"> 9</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="absolute_difference-10"><a href="#absolute_difference-10"><span class="linenos">10</span></a><span class="sd">    | $|22-34|=$ | $12$ |</span>
+</span><span id="absolute_difference-10"><a href="#absolute_difference-10"><span class="linenos">10</span></a><span class="sd">    | $\|22-34\|=$ | $12$ |</span>
 </span><span id="absolute_difference-11"><a href="#absolute_difference-11"><span class="linenos">11</span></a><span class="sd">    &quot;&quot;&quot;</span>
 </span><span id="absolute_difference-12"><a href="#absolute_difference-12"><span class="linenos">12</span></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">max_a</span><span class="p">,</span> <span class="n">max_a</span><span class="p">)</span>
 </span><span id="absolute_difference-13"><a href="#absolute_difference-13"><span class="linenos">13</span></a>    <span class="n">b</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">max_b</span><span class="p">,</span> <span class="n">max_b</span><span class="p">)</span>
@@ -616,9 +616,7 @@
 </thead>
 <tbody>
 <tr>
-  <td>$</td>
-  <td>22-34</td>
-  <td>=$</td>
+  <td>$|22-34|=$</td>
   <td>$12$</td>
 </tr>
 </tbody>
@@ -639,7 +637,7 @@
     </div>
     <a class="headerlink" href="#addition"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="addition-19"><a href="#addition-19"><span class="linenos">19</span></a><span class="k">def</span> <span class="nf">addition</span><span class="p">(</span><span class="n">max_sum</span><span class="o">=</span><span class="mi">99</span><span class="p">,</span> <span class="n">max_addend</span><span class="o">=</span><span class="mi">50</span><span class="p">):</span>
-</span><span id="addition-20"><a href="#addition-20"><span class="linenos">20</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Addition of two numbers</span>
+</span><span id="addition-20"><a href="#addition-20"><span class="linenos">20</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Addition of two numbers</span>
 </span><span id="addition-21"><a href="#addition-21"><span class="linenos">21</span></a>
 </span><span id="addition-22"><a href="#addition-22"><span class="linenos">22</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="addition-23"><a href="#addition-23"><span class="linenos">23</span></a><span class="sd">    | --- | --- |</span>
@@ -690,7 +688,7 @@
     </div>
     <a class="headerlink" href="#compare_fractions"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="compare_fractions-38"><a href="#compare_fractions-38"><span class="linenos">38</span></a><span class="k">def</span> <span class="nf">compare_fractions</span><span class="p">(</span><span class="n">max_val</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="compare_fractions-39"><a href="#compare_fractions-39"><span class="linenos">39</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Compare Fractions</span>
+</span><span id="compare_fractions-39"><a href="#compare_fractions-39"><span class="linenos">39</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Compare Fractions</span>
 </span><span id="compare_fractions-40"><a href="#compare_fractions-40"><span class="linenos">40</span></a>
 </span><span id="compare_fractions-41"><a href="#compare_fractions-41"><span class="linenos">41</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="compare_fractions-42"><a href="#compare_fractions-42"><span class="linenos">42</span></a><span class="sd">    | --- | --- |</span>
@@ -753,7 +751,7 @@
     </div>
     <a class="headerlink" href="#cube_root"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="cube_root-69"><a href="#cube_root-69"><span class="linenos">69</span></a><span class="k">def</span> <span class="nf">cube_root</span><span class="p">(</span><span class="n">min_no</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_no</span><span class="o">=</span><span class="mi">1000</span><span class="p">):</span>
-</span><span id="cube_root-70"><a href="#cube_root-70"><span class="linenos">70</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Cube Root</span>
+</span><span id="cube_root-70"><a href="#cube_root-70"><span class="linenos">70</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Cube Root</span>
 </span><span id="cube_root-71"><a href="#cube_root-71"><span class="linenos">71</span></a>
 </span><span id="cube_root-72"><a href="#cube_root-72"><span class="linenos">72</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="cube_root-73"><a href="#cube_root-73"><span class="linenos">73</span></a><span class="sd">    | --- | --- |</span>
@@ -762,7 +760,7 @@
 </span><span id="cube_root-76"><a href="#cube_root-76"><span class="linenos">76</span></a>    <span class="n">b</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="n">min_no</span><span class="p">,</span> <span class="n">max_no</span><span class="p">)</span>
 </span><span id="cube_root-77"><a href="#cube_root-77"><span class="linenos">77</span></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">b</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">3</span><span class="p">)</span>
 </span><span id="cube_root-78"><a href="#cube_root-78"><span class="linenos">78</span></a>
-</span><span id="cube_root-79"><a href="#cube_root-79"><span class="linenos">79</span></a>    <span class="k">return</span> <span class="p">(</span><span class="sa">rf</span><span class="s2">&quot;What is the cube root of: $\sqrt[3]</span><span class="se">{{</span><span class="si">{</span><span class="n">b</span><span class="si">}</span><span class="se">}}</span><span class="s2">=$ to 2 decimal places?&quot;</span><span class="p">,</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="nb">round</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span><span class="si">}</span><span class="s2">$&quot;</span><span class="p">)</span>
+</span><span id="cube_root-79"><a href="#cube_root-79"><span class="linenos">79</span></a>    <span class="k">return</span> <span class="p">(</span><span class="sa">rf</span><span class="s2">&quot;What is the cube root of: $\sqrt[3]</span><span class="se">{{</span><span class="si">{</span><span class="n">b</span><span class="si">}</span><span class="se">}}</span><span class="s2">=$ to 2 decimal places?&quot;</span><span class="p">,</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="nb">round</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="si">}</span><span class="s2">$&quot;</span><span class="p">)</span>
 </span></pre></div>
 
 
@@ -798,7 +796,7 @@
     </div>
     <a class="headerlink" href="#divide_fractions"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="divide_fractions-82"><a href="#divide_fractions-82"><span class="linenos"> 82</span></a><span class="k">def</span> <span class="nf">divide_fractions</span><span class="p">(</span><span class="n">max_val</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="divide_fractions-83"><a href="#divide_fractions-83"><span class="linenos"> 83</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Divide Fractions</span>
+</span><span id="divide_fractions-83"><a href="#divide_fractions-83"><span class="linenos"> 83</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Divide Fractions</span>
 </span><span id="divide_fractions-84"><a href="#divide_fractions-84"><span class="linenos"> 84</span></a>
 </span><span id="divide_fractions-85"><a href="#divide_fractions-85"><span class="linenos"> 85</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="divide_fractions-86"><a href="#divide_fractions-86"><span class="linenos"> 86</span></a><span class="sd">    | --- | --- |</span>
@@ -863,7 +861,7 @@
     </div>
     <a class="headerlink" href="#division"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="division-115"><a href="#division-115"><span class="linenos">115</span></a><span class="k">def</span> <span class="nf">division</span><span class="p">(</span><span class="n">max_a</span><span class="o">=</span><span class="mi">25</span><span class="p">,</span> <span class="n">max_b</span><span class="o">=</span><span class="mi">25</span><span class="p">):</span>
-</span><span id="division-116"><a href="#division-116"><span class="linenos">116</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Division</span>
+</span><span id="division-116"><a href="#division-116"><span class="linenos">116</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Division</span>
 </span><span id="division-117"><a href="#division-117"><span class="linenos">117</span></a>
 </span><span id="division-118"><a href="#division-118"><span class="linenos">118</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="division-119"><a href="#division-119"><span class="linenos">119</span></a><span class="sd">    | --- | --- |</span>
@@ -912,7 +910,7 @@
     </div>
     <a class="headerlink" href="#exponentiation"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="exponentiation-132"><a href="#exponentiation-132"><span class="linenos">132</span></a><span class="k">def</span> <span class="nf">exponentiation</span><span class="p">(</span><span class="n">max_base</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_expo</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="exponentiation-133"><a href="#exponentiation-133"><span class="linenos">133</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Exponentiation</span>
+</span><span id="exponentiation-133"><a href="#exponentiation-133"><span class="linenos">133</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Exponentiation</span>
 </span><span id="exponentiation-134"><a href="#exponentiation-134"><span class="linenos">134</span></a>
 </span><span id="exponentiation-135"><a href="#exponentiation-135"><span class="linenos">135</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="exponentiation-136"><a href="#exponentiation-136"><span class="linenos">136</span></a><span class="sd">    | --- | --- |</span>
@@ -957,7 +955,7 @@
     </div>
     <a class="headerlink" href="#factorial"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="factorial-145"><a href="#factorial-145"><span class="linenos">145</span></a><span class="k">def</span> <span class="nf">factorial</span><span class="p">(</span><span class="n">max_input</span><span class="o">=</span><span class="mi">6</span><span class="p">):</span>
-</span><span id="factorial-146"><a href="#factorial-146"><span class="linenos">146</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Factorial</span>
+</span><span id="factorial-146"><a href="#factorial-146"><span class="linenos">146</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Factorial</span>
 </span><span id="factorial-147"><a href="#factorial-147"><span class="linenos">147</span></a>
 </span><span id="factorial-148"><a href="#factorial-148"><span class="linenos">148</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="factorial-149"><a href="#factorial-149"><span class="linenos">149</span></a><span class="sd">    | --- | --- |</span>
@@ -1006,7 +1004,7 @@
     </div>
     <a class="headerlink" href="#fraction_multiplication"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="fraction_multiplication-162"><a href="#fraction_multiplication-162"><span class="linenos">162</span></a><span class="k">def</span> <span class="nf">fraction_multiplication</span><span class="p">(</span><span class="n">max_val</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="fraction_multiplication-163"><a href="#fraction_multiplication-163"><span class="linenos">163</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Fraction Multiplication</span>
+</span><span id="fraction_multiplication-163"><a href="#fraction_multiplication-163"><span class="linenos">163</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Fraction Multiplication</span>
 </span><span id="fraction_multiplication-164"><a href="#fraction_multiplication-164"><span class="linenos">164</span></a>
 </span><span id="fraction_multiplication-165"><a href="#fraction_multiplication-165"><span class="linenos">165</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="fraction_multiplication-166"><a href="#fraction_multiplication-166"><span class="linenos">166</span></a><span class="sd">    | --- | --- |</span>
@@ -1074,7 +1072,7 @@
     </div>
     <a class="headerlink" href="#fraction_to_decimal"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="fraction_to_decimal-198"><a href="#fraction_to_decimal-198"><span class="linenos">198</span></a><span class="k">def</span> <span class="nf">fraction_to_decimal</span><span class="p">(</span><span class="n">max_res</span><span class="o">=</span><span class="mi">99</span><span class="p">,</span> <span class="n">max_divid</span><span class="o">=</span><span class="mi">99</span><span class="p">):</span>
-</span><span id="fraction_to_decimal-199"><a href="#fraction_to_decimal-199"><span class="linenos">199</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Fraction to Decimal</span>
+</span><span id="fraction_to_decimal-199"><a href="#fraction_to_decimal-199"><span class="linenos">199</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Fraction to Decimal</span>
 </span><span id="fraction_to_decimal-200"><a href="#fraction_to_decimal-200"><span class="linenos">200</span></a>
 </span><span id="fraction_to_decimal-201"><a href="#fraction_to_decimal-201"><span class="linenos">201</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="fraction_to_decimal-202"><a href="#fraction_to_decimal-202"><span class="linenos">202</span></a><span class="sd">    | --- | --- |</span>
@@ -1120,7 +1118,7 @@
     </div>
     <a class="headerlink" href="#greatest_common_divisor"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="greatest_common_divisor-212"><a href="#greatest_common_divisor-212"><span class="linenos">212</span></a><span class="k">def</span> <span class="nf">greatest_common_divisor</span><span class="p">(</span><span class="n">numbers_count</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">max_num</span><span class="o">=</span><span class="mi">10</span><span class="o">**</span><span class="mi">3</span><span class="p">):</span>
-</span><span id="greatest_common_divisor-213"><a href="#greatest_common_divisor-213"><span class="linenos">213</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Greatest Common Divisor of N Numbers ( GCD / HCF )</span>
+</span><span id="greatest_common_divisor-213"><a href="#greatest_common_divisor-213"><span class="linenos">213</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Greatest Common Divisor of N Numbers ( GCD / HCF )</span>
 </span><span id="greatest_common_divisor-214"><a href="#greatest_common_divisor-214"><span class="linenos">214</span></a>
 </span><span id="greatest_common_divisor-215"><a href="#greatest_common_divisor-215"><span class="linenos">215</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="greatest_common_divisor-216"><a href="#greatest_common_divisor-216"><span class="linenos">216</span></a><span class="sd">    | --- | --- |</span>
@@ -1145,7 +1143,7 @@
 </span><span id="greatest_common_divisor-235"><a href="#greatest_common_divisor-235"><span class="linenos">235</span></a>        <span class="n">greatestCommonDivisor</span> <span class="o">=</span> <span class="n">greatestCommonDivisorOfTwoNumbers</span><span class="p">(</span>
 </span><span id="greatest_common_divisor-236"><a href="#greatest_common_divisor-236"><span class="linenos">236</span></a>            <span class="n">numbers</span><span class="p">[</span><span class="n">index</span><span class="p">],</span> <span class="n">greatestCommonDivisor</span><span class="p">)</span>
 </span><span id="greatest_common_divisor-237"><a href="#greatest_common_divisor-237"><span class="linenos">237</span></a>
-</span><span id="greatest_common_divisor-238"><a href="#greatest_common_divisor-238"><span class="linenos">238</span></a>    <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;$GCD(</span><span class="si">{</span><span class="s2">&quot;,&quot;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="n">numbers</span><span class="p">))</span><span class="si">}</span><span class="s1">)=$&#39;</span><span class="p">,</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">greatestCommonDivisor</span><span class="si">}</span><span class="s2">$&quot;</span>
+</span><span id="greatest_common_divisor-238"><a href="#greatest_common_divisor-238"><span class="linenos">238</span></a>    <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;$GCD(</span><span class="si">{</span><span class="s2">&quot;,&quot;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span><span class="w"> </span><span class="n">numbers</span><span class="p">))</span><span class="si">}</span><span class="s1">)=$&#39;</span><span class="p">,</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">greatestCommonDivisor</span><span class="si">}</span><span class="s2">$&quot;</span>
 </span></pre></div>
 
 
@@ -1181,7 +1179,7 @@
     </div>
     <a class="headerlink" href="#is_composite"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="is_composite-241"><a href="#is_composite-241"><span class="linenos">241</span></a><span class="k">def</span> <span class="nf">is_composite</span><span class="p">(</span><span class="n">max_num</span><span class="o">=</span><span class="mi">250</span><span class="p">):</span>
-</span><span id="is_composite-242"><a href="#is_composite-242"><span class="linenos">242</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Is Composite</span>
+</span><span id="is_composite-242"><a href="#is_composite-242"><span class="linenos">242</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Is Composite</span>
 </span><span id="is_composite-243"><a href="#is_composite-243"><span class="linenos">243</span></a>
 </span><span id="is_composite-244"><a href="#is_composite-244"><span class="linenos">244</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="is_composite-245"><a href="#is_composite-245"><span class="linenos">245</span></a><span class="sd">    | --- | --- |</span>
@@ -1233,7 +1231,7 @@
     </div>
     <a class="headerlink" href="#is_prime"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="is_prime-261"><a href="#is_prime-261"><span class="linenos">261</span></a><span class="k">def</span> <span class="nf">is_prime</span><span class="p">(</span><span class="n">max_num</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="is_prime-262"><a href="#is_prime-262"><span class="linenos">262</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Is Prime</span>
+</span><span id="is_prime-262"><a href="#is_prime-262"><span class="linenos">262</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Is Prime</span>
 </span><span id="is_prime-263"><a href="#is_prime-263"><span class="linenos">263</span></a>
 </span><span id="is_prime-264"><a href="#is_prime-264"><span class="linenos">264</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="is_prime-265"><a href="#is_prime-265"><span class="linenos">265</span></a><span class="sd">    | --- | --- |</span>
@@ -1286,7 +1284,7 @@
     </div>
     <a class="headerlink" href="#multiplication"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="multiplication-282"><a href="#multiplication-282"><span class="linenos">282</span></a><span class="k">def</span> <span class="nf">multiplication</span><span class="p">(</span><span class="n">max_multi</span><span class="o">=</span><span class="mi">12</span><span class="p">):</span>
-</span><span id="multiplication-283"><a href="#multiplication-283"><span class="linenos">283</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Multiplication</span>
+</span><span id="multiplication-283"><a href="#multiplication-283"><span class="linenos">283</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Multiplication</span>
 </span><span id="multiplication-284"><a href="#multiplication-284"><span class="linenos">284</span></a>
 </span><span id="multiplication-285"><a href="#multiplication-285"><span class="linenos">285</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="multiplication-286"><a href="#multiplication-286"><span class="linenos">286</span></a><span class="sd">    | --- | --- |</span>
@@ -1332,7 +1330,7 @@
     </div>
     <a class="headerlink" href="#percentage"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="percentage-296"><a href="#percentage-296"><span class="linenos">296</span></a><span class="k">def</span> <span class="nf">percentage</span><span class="p">(</span><span class="n">max_value</span><span class="o">=</span><span class="mi">99</span><span class="p">,</span> <span class="n">max_percentage</span><span class="o">=</span><span class="mi">99</span><span class="p">):</span>
-</span><span id="percentage-297"><a href="#percentage-297"><span class="linenos">297</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Percentage of a number</span>
+</span><span id="percentage-297"><a href="#percentage-297"><span class="linenos">297</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Percentage of a number</span>
 </span><span id="percentage-298"><a href="#percentage-298"><span class="linenos">298</span></a>
 </span><span id="percentage-299"><a href="#percentage-299"><span class="linenos">299</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="percentage-300"><a href="#percentage-300"><span class="linenos">300</span></a><span class="sd">    | --- | --- |</span>
@@ -1381,7 +1379,7 @@
     </div>
     <a class="headerlink" href="#percentage_difference"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="percentage_difference-313"><a href="#percentage_difference-313"><span class="linenos">313</span></a><span class="k">def</span> <span class="nf">percentage_difference</span><span class="p">(</span><span class="n">max_value</span><span class="o">=</span><span class="mi">200</span><span class="p">,</span> <span class="n">min_value</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
-</span><span id="percentage_difference-314"><a href="#percentage_difference-314"><span class="linenos">314</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Percentage difference between two numbers</span>
+</span><span id="percentage_difference-314"><a href="#percentage_difference-314"><span class="linenos">314</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Percentage difference between two numbers</span>
 </span><span id="percentage_difference-315"><a href="#percentage_difference-315"><span class="linenos">315</span></a>
 </span><span id="percentage_difference-316"><a href="#percentage_difference-316"><span class="linenos">316</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="percentage_difference-317"><a href="#percentage_difference-317"><span class="linenos">317</span></a><span class="sd">    | --- | --- |</span>
@@ -1431,7 +1429,7 @@
     </div>
     <a class="headerlink" href="#percentage_error"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="percentage_error-331"><a href="#percentage_error-331"><span class="linenos">331</span></a><span class="k">def</span> <span class="nf">percentage_error</span><span class="p">(</span><span class="n">max_value</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">min_value</span><span class="o">=-</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="percentage_error-332"><a href="#percentage_error-332"><span class="linenos">332</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Percentage error</span>
+</span><span id="percentage_error-332"><a href="#percentage_error-332"><span class="linenos">332</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Percentage error</span>
 </span><span id="percentage_error-333"><a href="#percentage_error-333"><span class="linenos">333</span></a>
 </span><span id="percentage_error-334"><a href="#percentage_error-334"><span class="linenos">334</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="percentage_error-335"><a href="#percentage_error-335"><span class="linenos">335</span></a><span class="sd">    | --- | --- |</span>
@@ -1484,7 +1482,7 @@
     </div>
     <a class="headerlink" href="#power_of_powers"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="power_of_powers-352"><a href="#power_of_powers-352"><span class="linenos">352</span></a><span class="k">def</span> <span class="nf">power_of_powers</span><span class="p">(</span><span class="n">max_base</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">max_power</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="power_of_powers-353"><a href="#power_of_powers-353"><span class="linenos">353</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Power of Powers</span>
+</span><span id="power_of_powers-353"><a href="#power_of_powers-353"><span class="linenos">353</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Power of Powers</span>
 </span><span id="power_of_powers-354"><a href="#power_of_powers-354"><span class="linenos">354</span></a>
 </span><span id="power_of_powers-355"><a href="#power_of_powers-355"><span class="linenos">355</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="power_of_powers-356"><a href="#power_of_powers-356"><span class="linenos">356</span></a><span class="sd">    | --- | --- |</span>
@@ -1533,7 +1531,7 @@
     </div>
     <a class="headerlink" href="#square"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="square-369"><a href="#square-369"><span class="linenos">369</span></a><span class="k">def</span> <span class="nf">square</span><span class="p">(</span><span class="n">max_square_num</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="square-370"><a href="#square-370"><span class="linenos">370</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Square</span>
+</span><span id="square-370"><a href="#square-370"><span class="linenos">370</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Square</span>
 </span><span id="square-371"><a href="#square-371"><span class="linenos">371</span></a>
 </span><span id="square-372"><a href="#square-372"><span class="linenos">372</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="square-373"><a href="#square-373"><span class="linenos">373</span></a><span class="sd">    | --- | --- |</span>
@@ -1578,7 +1576,7 @@
     </div>
     <a class="headerlink" href="#square_root"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="square_root-382"><a href="#square_root-382"><span class="linenos">382</span></a><span class="k">def</span> <span class="nf">square_root</span><span class="p">(</span><span class="n">min_no</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_no</span><span class="o">=</span><span class="mi">12</span><span class="p">):</span>
-</span><span id="square_root-383"><a href="#square_root-383"><span class="linenos">383</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Square Root</span>
+</span><span id="square_root-383"><a href="#square_root-383"><span class="linenos">383</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Square Root</span>
 </span><span id="square_root-384"><a href="#square_root-384"><span class="linenos">384</span></a>
 </span><span id="square_root-385"><a href="#square_root-385"><span class="linenos">385</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="square_root-386"><a href="#square_root-386"><span class="linenos">386</span></a><span class="sd">    | --- | --- |</span>
@@ -1623,7 +1621,7 @@
     </div>
     <a class="headerlink" href="#simplify_square_root"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="simplify_square_root-395"><a href="#simplify_square_root-395"><span class="linenos">395</span></a><span class="k">def</span> <span class="nf">simplify_square_root</span><span class="p">(</span><span class="n">max_variable</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="simplify_square_root-396"><a href="#simplify_square_root-396"><span class="linenos">396</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Simplify Square Root</span>
+</span><span id="simplify_square_root-396"><a href="#simplify_square_root-396"><span class="linenos">396</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Simplify Square Root</span>
 </span><span id="simplify_square_root-397"><a href="#simplify_square_root-397"><span class="linenos">397</span></a>
 </span><span id="simplify_square_root-398"><a href="#simplify_square_root-398"><span class="linenos">398</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="simplify_square_root-399"><a href="#simplify_square_root-399"><span class="linenos">399</span></a><span class="sd">    | --- | --- |</span>
@@ -1686,7 +1684,7 @@
     </div>
     <a class="headerlink" href="#subtraction"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="subtraction-426"><a href="#subtraction-426"><span class="linenos">426</span></a><span class="k">def</span> <span class="nf">subtraction</span><span class="p">(</span><span class="n">max_minuend</span><span class="o">=</span><span class="mi">99</span><span class="p">,</span> <span class="n">max_diff</span><span class="o">=</span><span class="mi">99</span><span class="p">):</span>
-</span><span id="subtraction-427"><a href="#subtraction-427"><span class="linenos">427</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Subtraction of two numbers</span>
+</span><span id="subtraction-427"><a href="#subtraction-427"><span class="linenos">427</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Subtraction of two numbers</span>
 </span><span id="subtraction-428"><a href="#subtraction-428"><span class="linenos">428</span></a>
 </span><span id="subtraction-429"><a href="#subtraction-429"><span class="linenos">429</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="subtraction-430"><a href="#subtraction-430"><span class="linenos">430</span></a><span class="sd">    | --- | --- |</span>
@@ -1840,7 +1838,7 @@
                         if (doc.annotation)
                             heading += `<span class="annotation">${doc.annotation}</span>`;
                         if (doc.default_value)
-                            heading += `<span class="default_value">${doc.default_value}</span>`;
+                            heading += `<span class="default_value"> = ${doc.default_value}</span>`;
                         break;
                     default:
                         heading = `<span class="name">${doc.fullname}</span>`;
diff --git a/docs/mathgenerator/calculus.html b/docs/mathgenerator/calculus.html
index c10000c..f789f4e 100644
--- a/docs/mathgenerator/calculus.html
+++ b/docs/mathgenerator/calculus.html
@@ -3,14 +3,14 @@
 <head>
     <meta charset="utf-8">
     <meta name="viewport" content="width=device-width, initial-scale=1">
-    <meta name="generator" content="pdoc 12.3.0"/>
+    <meta name="generator" content="pdoc 13.1.1"/>
     <title>mathgenerator.calculus API documentation</title>
 
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@@ -50,8 +50,8 @@
 
 
 
-        <h2>API Documentation</h2>
-            <ul class="memberlist">
+            <h2>API Documentation</h2>
+                <ul class="memberlist">
             <li>
                     <a class="function" href="#definite_integral">definite_integral</a>
             </li>
@@ -94,7 +94,7 @@
 </span><span id="L-4"><a href="#L-4"><span class="linenos">  4</span></a>
 </span><span id="L-5"><a href="#L-5"><span class="linenos">  5</span></a>
 </span><span id="L-6"><a href="#L-6"><span class="linenos">  6</span></a><span class="k">def</span> <span class="nf">definite_integral</span><span class="p">(</span><span class="n">max_coef</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="L-7"><a href="#L-7"><span class="linenos">  7</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Definite Integral of Quadratic Equation</span>
+</span><span id="L-7"><a href="#L-7"><span class="linenos">  7</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Definite Integral of Quadratic Equation</span>
 </span><span id="L-8"><a href="#L-8"><span class="linenos">  8</span></a>
 </span><span id="L-9"><a href="#L-9"><span class="linenos">  9</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-10"><a href="#L-10"><span class="linenos"> 10</span></a><span class="sd">    | --- | --- |</span>
@@ -117,7 +117,7 @@
 </span><span id="L-27"><a href="#L-27"><span class="linenos"> 27</span></a><span class="k">def</span> <span class="nf">power_rule_differentiation</span><span class="p">(</span><span class="n">max_coef</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
 </span><span id="L-28"><a href="#L-28"><span class="linenos"> 28</span></a>                               <span class="n">max_exp</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
 </span><span id="L-29"><a href="#L-29"><span class="linenos"> 29</span></a>                               <span class="n">max_terms</span><span class="o">=</span><span class="mi">5</span><span class="p">):</span>
-</span><span id="L-30"><a href="#L-30"><span class="linenos"> 30</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Power Rule Differentiation</span>
+</span><span id="L-30"><a href="#L-30"><span class="linenos"> 30</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Power Rule Differentiation</span>
 </span><span id="L-31"><a href="#L-31"><span class="linenos"> 31</span></a>
 </span><span id="L-32"><a href="#L-32"><span class="linenos"> 32</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-33"><a href="#L-33"><span class="linenos"> 33</span></a><span class="sd">    | --- | --- |</span>
@@ -135,7 +135,7 @@
 </span><span id="L-45"><a href="#L-45"><span class="linenos"> 45</span></a>        <span class="n">exponent</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_exp</span><span class="p">)</span>
 </span><span id="L-46"><a href="#L-46"><span class="linenos"> 46</span></a>
 </span><span id="L-47"><a href="#L-47"><span class="linenos"> 47</span></a>        <span class="n">problem</span> <span class="o">+=</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">coefficient</span><span class="si">}</span><span class="s1">x^</span><span class="se">{{</span><span class="si">{</span><span class="n">exponent</span><span class="si">}</span><span class="se">}}</span><span class="s1">&#39;</span>
-</span><span id="L-48"><a href="#L-48"><span class="linenos"> 48</span></a>        <span class="n">solution</span> <span class="o">+=</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">coefficient</span> <span class="o">*</span> <span class="n">exponent</span><span class="si">}</span><span class="s1">x^</span><span class="se">{{</span><span class="si">{</span><span class="n">exponent</span> <span class="o">-</span> <span class="mi">1</span><span class="si">}</span><span class="se">}}</span><span class="s1">&#39;</span>
+</span><span id="L-48"><a href="#L-48"><span class="linenos"> 48</span></a>        <span class="n">solution</span> <span class="o">+=</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">coefficient</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">exponent</span><span class="si">}</span><span class="s1">x^</span><span class="se">{{</span><span class="si">{</span><span class="n">exponent</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="si">}</span><span class="se">}}</span><span class="s1">&#39;</span>
 </span><span id="L-49"><a href="#L-49"><span class="linenos"> 49</span></a>
 </span><span id="L-50"><a href="#L-50"><span class="linenos"> 50</span></a>    <span class="k">return</span> <span class="n">problem</span> <span class="o">+</span> <span class="s1">&#39;$&#39;</span><span class="p">,</span> <span class="n">solution</span> <span class="o">+</span> <span class="s1">&#39;$&#39;</span>
 </span><span id="L-51"><a href="#L-51"><span class="linenos"> 51</span></a>
@@ -143,7 +143,7 @@
 </span><span id="L-53"><a href="#L-53"><span class="linenos"> 53</span></a><span class="k">def</span> <span class="nf">power_rule_integration</span><span class="p">(</span><span class="n">max_coef</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
 </span><span id="L-54"><a href="#L-54"><span class="linenos"> 54</span></a>                           <span class="n">max_exp</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
 </span><span id="L-55"><a href="#L-55"><span class="linenos"> 55</span></a>                           <span class="n">max_terms</span><span class="o">=</span><span class="mi">5</span><span class="p">):</span>
-</span><span id="L-56"><a href="#L-56"><span class="linenos"> 56</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Power Rule Integration</span>
+</span><span id="L-56"><a href="#L-56"><span class="linenos"> 56</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Power Rule Integration</span>
 </span><span id="L-57"><a href="#L-57"><span class="linenos"> 57</span></a>
 </span><span id="L-58"><a href="#L-58"><span class="linenos"> 58</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-59"><a href="#L-59"><span class="linenos"> 59</span></a><span class="sd">    | --- | --- |</span>
@@ -161,7 +161,7 @@
 </span><span id="L-71"><a href="#L-71"><span class="linenos"> 71</span></a>        <span class="n">exponent</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_exp</span><span class="p">)</span>
 </span><span id="L-72"><a href="#L-72"><span class="linenos"> 72</span></a>
 </span><span id="L-73"><a href="#L-73"><span class="linenos"> 73</span></a>        <span class="n">problem</span> <span class="o">+=</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">coefficient</span><span class="si">}</span><span class="s1">x^</span><span class="se">{{</span><span class="si">{</span><span class="n">exponent</span><span class="si">}</span><span class="se">}}</span><span class="s1">&#39;</span>
-</span><span id="L-74"><a href="#L-74"><span class="linenos"> 74</span></a>        <span class="n">solution</span> <span class="o">+=</span> <span class="sa">rf</span><span class="s1">&#39;\frac</span><span class="se">{{</span><span class="si">{</span><span class="n">coefficient</span><span class="si">}</span><span class="se">}}{{</span><span class="si">{</span><span class="n">exponent</span><span class="si">}</span><span class="se">}}</span><span class="s1">x^</span><span class="se">{{</span><span class="si">{</span><span class="n">exponent</span> <span class="o">+</span> <span class="mi">1</span><span class="si">}</span><span class="se">}}</span><span class="s1">&#39;</span>
+</span><span id="L-74"><a href="#L-74"><span class="linenos"> 74</span></a>        <span class="n">solution</span> <span class="o">+=</span> <span class="sa">rf</span><span class="s1">&#39;\frac</span><span class="se">{{</span><span class="si">{</span><span class="n">coefficient</span><span class="si">}</span><span class="se">}}{{</span><span class="si">{</span><span class="n">exponent</span><span class="si">}</span><span class="se">}}</span><span class="s1">x^</span><span class="se">{{</span><span class="si">{</span><span class="n">exponent</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="si">}</span><span class="se">}}</span><span class="s1">&#39;</span>
 </span><span id="L-75"><a href="#L-75"><span class="linenos"> 75</span></a>
 </span><span id="L-76"><a href="#L-76"><span class="linenos"> 76</span></a>    <span class="n">solution</span> <span class="o">+=</span> <span class="s2">&quot; + C&quot;</span>
 </span><span id="L-77"><a href="#L-77"><span class="linenos"> 77</span></a>
@@ -169,11 +169,11 @@
 </span><span id="L-79"><a href="#L-79"><span class="linenos"> 79</span></a>
 </span><span id="L-80"><a href="#L-80"><span class="linenos"> 80</span></a>
 </span><span id="L-81"><a href="#L-81"><span class="linenos"> 81</span></a><span class="k">def</span> <span class="nf">stationary_points</span><span class="p">(</span><span class="n">max_exp</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">max_coef</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-82"><a href="#L-82"><span class="linenos"> 82</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Stationary Points</span>
+</span><span id="L-82"><a href="#L-82"><span class="linenos"> 82</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Stationary Points</span>
 </span><span id="L-83"><a href="#L-83"><span class="linenos"> 83</span></a>
 </span><span id="L-84"><a href="#L-84"><span class="linenos"> 84</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-85"><a href="#L-85"><span class="linenos"> 85</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="L-86"><a href="#L-86"><span class="linenos"> 86</span></a><span class="sd">    | $f(x)=6*x^3 + 6*x^2 + x + 8$ | ${- \frac{1}{3} - \frac{\sqrt{2}}{6}, - \frac{1}{3} + \frac{\sqrt{2}}{6}}$ |</span>
+</span><span id="L-86"><a href="#L-86"><span class="linenos"> 86</span></a><span class="sd">    | $f(x)=6x^3 + 6x^2 + x + 8$ | ${- \frac{1}{3} - \frac{\sqrt{2}}{6}, - \frac{1}{3} + \frac{\sqrt{2}}{6}}$ |</span>
 </span><span id="L-87"><a href="#L-87"><span class="linenos"> 87</span></a><span class="sd">    &quot;&quot;&quot;</span>
 </span><span id="L-88"><a href="#L-88"><span class="linenos"> 88</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="s1">&#39;&#39;</span>
 </span><span id="L-89"><a href="#L-89"><span class="linenos"> 89</span></a>    <span class="k">while</span> <span class="nb">len</span><span class="p">(</span><span class="n">solution</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
@@ -184,12 +184,12 @@
 </span><span id="L-94"><a href="#L-94"><span class="linenos"> 94</span></a>            <span class="n">problem</span> <span class="o">+=</span> <span class="n">coefficient</span> <span class="o">*</span> <span class="nb">pow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">exp</span><span class="p">)</span>
 </span><span id="L-95"><a href="#L-95"><span class="linenos"> 95</span></a>        <span class="n">solution</span> <span class="o">=</span> <span class="n">sympy</span><span class="o">.</span><span class="n">stationary_points</span><span class="p">(</span><span class="n">problem</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
 </span><span id="L-96"><a href="#L-96"><span class="linenos"> 96</span></a>
-</span><span id="L-97"><a href="#L-97"><span class="linenos"> 97</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="s1">&#39;f(x)=&#39;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">problem</span><span class="p">)</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="s1">&#39;**&#39;</span><span class="p">,</span> <span class="s1">&#39;^&#39;</span><span class="p">)</span>
+</span><span id="L-97"><a href="#L-97"><span class="linenos"> 97</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="s1">&#39;f(x)=&#39;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">problem</span><span class="p">)</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="s1">&#39;**&#39;</span><span class="p">,</span> <span class="s1">&#39;^&#39;</span><span class="p">)</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="s1">&#39;*&#39;</span><span class="p">,</span><span class="s1">&#39;&#39;</span><span class="p">)</span>
 </span><span id="L-98"><a href="#L-98"><span class="linenos"> 98</span></a>    <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="n">problem</span><span class="si">}</span><span class="s1">$&#39;</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="n">sympy</span><span class="o">.</span><span class="n">latex</span><span class="p">(</span><span class="n">solution</span><span class="p">)[</span><span class="mi">6</span><span class="p">:</span><span class="o">-</span><span class="mi">8</span><span class="p">]</span><span class="si">}</span><span class="se">}}</span><span class="s1">$&#39;</span>
 </span><span id="L-99"><a href="#L-99"><span class="linenos"> 99</span></a>
 </span><span id="L-100"><a href="#L-100"><span class="linenos">100</span></a>
 </span><span id="L-101"><a href="#L-101"><span class="linenos">101</span></a><span class="k">def</span> <span class="nf">trig_differentiation</span><span class="p">():</span>
-</span><span id="L-102"><a href="#L-102"><span class="linenos">102</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Trigonometric Differentiation</span>
+</span><span id="L-102"><a href="#L-102"><span class="linenos">102</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Trigonometric Differentiation</span>
 </span><span id="L-103"><a href="#L-103"><span class="linenos">103</span></a>
 </span><span id="L-104"><a href="#L-104"><span class="linenos">104</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-105"><a href="#L-105"><span class="linenos">105</span></a><span class="sd">    | --- | --- |</span>
@@ -224,7 +224,7 @@
     </div>
     <a class="headerlink" href="#definite_integral"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="definite_integral-7"><a href="#definite_integral-7"><span class="linenos"> 7</span></a><span class="k">def</span> <span class="nf">definite_integral</span><span class="p">(</span><span class="n">max_coef</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="definite_integral-8"><a href="#definite_integral-8"><span class="linenos"> 8</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Definite Integral of Quadratic Equation</span>
+</span><span id="definite_integral-8"><a href="#definite_integral-8"><span class="linenos"> 8</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Definite Integral of Quadratic Equation</span>
 </span><span id="definite_integral-9"><a href="#definite_integral-9"><span class="linenos"> 9</span></a>
 </span><span id="definite_integral-10"><a href="#definite_integral-10"><span class="linenos">10</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="definite_integral-11"><a href="#definite_integral-11"><span class="linenos">11</span></a><span class="sd">    | --- | --- |</span>
@@ -279,7 +279,7 @@
             <div class="pdoc-code codehilite"><pre><span></span><span id="power_rule_differentiation-28"><a href="#power_rule_differentiation-28"><span class="linenos">28</span></a><span class="k">def</span> <span class="nf">power_rule_differentiation</span><span class="p">(</span><span class="n">max_coef</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
 </span><span id="power_rule_differentiation-29"><a href="#power_rule_differentiation-29"><span class="linenos">29</span></a>                               <span class="n">max_exp</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
 </span><span id="power_rule_differentiation-30"><a href="#power_rule_differentiation-30"><span class="linenos">30</span></a>                               <span class="n">max_terms</span><span class="o">=</span><span class="mi">5</span><span class="p">):</span>
-</span><span id="power_rule_differentiation-31"><a href="#power_rule_differentiation-31"><span class="linenos">31</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Power Rule Differentiation</span>
+</span><span id="power_rule_differentiation-31"><a href="#power_rule_differentiation-31"><span class="linenos">31</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Power Rule Differentiation</span>
 </span><span id="power_rule_differentiation-32"><a href="#power_rule_differentiation-32"><span class="linenos">32</span></a>
 </span><span id="power_rule_differentiation-33"><a href="#power_rule_differentiation-33"><span class="linenos">33</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="power_rule_differentiation-34"><a href="#power_rule_differentiation-34"><span class="linenos">34</span></a><span class="sd">    | --- | --- |</span>
@@ -297,7 +297,7 @@
 </span><span id="power_rule_differentiation-46"><a href="#power_rule_differentiation-46"><span class="linenos">46</span></a>        <span class="n">exponent</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_exp</span><span class="p">)</span>
 </span><span id="power_rule_differentiation-47"><a href="#power_rule_differentiation-47"><span class="linenos">47</span></a>
 </span><span id="power_rule_differentiation-48"><a href="#power_rule_differentiation-48"><span class="linenos">48</span></a>        <span class="n">problem</span> <span class="o">+=</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">coefficient</span><span class="si">}</span><span class="s1">x^</span><span class="se">{{</span><span class="si">{</span><span class="n">exponent</span><span class="si">}</span><span class="se">}}</span><span class="s1">&#39;</span>
-</span><span id="power_rule_differentiation-49"><a href="#power_rule_differentiation-49"><span class="linenos">49</span></a>        <span class="n">solution</span> <span class="o">+=</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">coefficient</span> <span class="o">*</span> <span class="n">exponent</span><span class="si">}</span><span class="s1">x^</span><span class="se">{{</span><span class="si">{</span><span class="n">exponent</span> <span class="o">-</span> <span class="mi">1</span><span class="si">}</span><span class="se">}}</span><span class="s1">&#39;</span>
+</span><span id="power_rule_differentiation-49"><a href="#power_rule_differentiation-49"><span class="linenos">49</span></a>        <span class="n">solution</span> <span class="o">+=</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">coefficient</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">exponent</span><span class="si">}</span><span class="s1">x^</span><span class="se">{{</span><span class="si">{</span><span class="n">exponent</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="si">}</span><span class="se">}}</span><span class="s1">&#39;</span>
 </span><span id="power_rule_differentiation-50"><a href="#power_rule_differentiation-50"><span class="linenos">50</span></a>
 </span><span id="power_rule_differentiation-51"><a href="#power_rule_differentiation-51"><span class="linenos">51</span></a>    <span class="k">return</span> <span class="n">problem</span> <span class="o">+</span> <span class="s1">&#39;$&#39;</span><span class="p">,</span> <span class="n">solution</span> <span class="o">+</span> <span class="s1">&#39;$&#39;</span>
 </span></pre></div>
@@ -337,7 +337,7 @@
             <div class="pdoc-code codehilite"><pre><span></span><span id="power_rule_integration-54"><a href="#power_rule_integration-54"><span class="linenos">54</span></a><span class="k">def</span> <span class="nf">power_rule_integration</span><span class="p">(</span><span class="n">max_coef</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
 </span><span id="power_rule_integration-55"><a href="#power_rule_integration-55"><span class="linenos">55</span></a>                           <span class="n">max_exp</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
 </span><span id="power_rule_integration-56"><a href="#power_rule_integration-56"><span class="linenos">56</span></a>                           <span class="n">max_terms</span><span class="o">=</span><span class="mi">5</span><span class="p">):</span>
-</span><span id="power_rule_integration-57"><a href="#power_rule_integration-57"><span class="linenos">57</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Power Rule Integration</span>
+</span><span id="power_rule_integration-57"><a href="#power_rule_integration-57"><span class="linenos">57</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Power Rule Integration</span>
 </span><span id="power_rule_integration-58"><a href="#power_rule_integration-58"><span class="linenos">58</span></a>
 </span><span id="power_rule_integration-59"><a href="#power_rule_integration-59"><span class="linenos">59</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="power_rule_integration-60"><a href="#power_rule_integration-60"><span class="linenos">60</span></a><span class="sd">    | --- | --- |</span>
@@ -355,7 +355,7 @@
 </span><span id="power_rule_integration-72"><a href="#power_rule_integration-72"><span class="linenos">72</span></a>        <span class="n">exponent</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_exp</span><span class="p">)</span>
 </span><span id="power_rule_integration-73"><a href="#power_rule_integration-73"><span class="linenos">73</span></a>
 </span><span id="power_rule_integration-74"><a href="#power_rule_integration-74"><span class="linenos">74</span></a>        <span class="n">problem</span> <span class="o">+=</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">coefficient</span><span class="si">}</span><span class="s1">x^</span><span class="se">{{</span><span class="si">{</span><span class="n">exponent</span><span class="si">}</span><span class="se">}}</span><span class="s1">&#39;</span>
-</span><span id="power_rule_integration-75"><a href="#power_rule_integration-75"><span class="linenos">75</span></a>        <span class="n">solution</span> <span class="o">+=</span> <span class="sa">rf</span><span class="s1">&#39;\frac</span><span class="se">{{</span><span class="si">{</span><span class="n">coefficient</span><span class="si">}</span><span class="se">}}{{</span><span class="si">{</span><span class="n">exponent</span><span class="si">}</span><span class="se">}}</span><span class="s1">x^</span><span class="se">{{</span><span class="si">{</span><span class="n">exponent</span> <span class="o">+</span> <span class="mi">1</span><span class="si">}</span><span class="se">}}</span><span class="s1">&#39;</span>
+</span><span id="power_rule_integration-75"><a href="#power_rule_integration-75"><span class="linenos">75</span></a>        <span class="n">solution</span> <span class="o">+=</span> <span class="sa">rf</span><span class="s1">&#39;\frac</span><span class="se">{{</span><span class="si">{</span><span class="n">coefficient</span><span class="si">}</span><span class="se">}}{{</span><span class="si">{</span><span class="n">exponent</span><span class="si">}</span><span class="se">}}</span><span class="s1">x^</span><span class="se">{{</span><span class="si">{</span><span class="n">exponent</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="si">}</span><span class="se">}}</span><span class="s1">&#39;</span>
 </span><span id="power_rule_integration-76"><a href="#power_rule_integration-76"><span class="linenos">76</span></a>
 </span><span id="power_rule_integration-77"><a href="#power_rule_integration-77"><span class="linenos">77</span></a>    <span class="n">solution</span> <span class="o">+=</span> <span class="s2">&quot; + C&quot;</span>
 </span><span id="power_rule_integration-78"><a href="#power_rule_integration-78"><span class="linenos">78</span></a>
@@ -395,11 +395,11 @@
     </div>
     <a class="headerlink" href="#stationary_points"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="stationary_points-82"><a href="#stationary_points-82"><span class="linenos">82</span></a><span class="k">def</span> <span class="nf">stationary_points</span><span class="p">(</span><span class="n">max_exp</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">max_coef</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="stationary_points-83"><a href="#stationary_points-83"><span class="linenos">83</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Stationary Points</span>
+</span><span id="stationary_points-83"><a href="#stationary_points-83"><span class="linenos">83</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Stationary Points</span>
 </span><span id="stationary_points-84"><a href="#stationary_points-84"><span class="linenos">84</span></a>
 </span><span id="stationary_points-85"><a href="#stationary_points-85"><span class="linenos">85</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="stationary_points-86"><a href="#stationary_points-86"><span class="linenos">86</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="stationary_points-87"><a href="#stationary_points-87"><span class="linenos">87</span></a><span class="sd">    | $f(x)=6*x^3 + 6*x^2 + x + 8$ | ${- \frac{1}{3} - \frac{\sqrt{2}}{6}, - \frac{1}{3} + \frac{\sqrt{2}}{6}}$ |</span>
+</span><span id="stationary_points-87"><a href="#stationary_points-87"><span class="linenos">87</span></a><span class="sd">    | $f(x)=6x^3 + 6x^2 + x + 8$ | ${- \frac{1}{3} - \frac{\sqrt{2}}{6}, - \frac{1}{3} + \frac{\sqrt{2}}{6}}$ |</span>
 </span><span id="stationary_points-88"><a href="#stationary_points-88"><span class="linenos">88</span></a><span class="sd">    &quot;&quot;&quot;</span>
 </span><span id="stationary_points-89"><a href="#stationary_points-89"><span class="linenos">89</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="s1">&#39;&#39;</span>
 </span><span id="stationary_points-90"><a href="#stationary_points-90"><span class="linenos">90</span></a>    <span class="k">while</span> <span class="nb">len</span><span class="p">(</span><span class="n">solution</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
@@ -410,7 +410,7 @@
 </span><span id="stationary_points-95"><a href="#stationary_points-95"><span class="linenos">95</span></a>            <span class="n">problem</span> <span class="o">+=</span> <span class="n">coefficient</span> <span class="o">*</span> <span class="nb">pow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">exp</span><span class="p">)</span>
 </span><span id="stationary_points-96"><a href="#stationary_points-96"><span class="linenos">96</span></a>        <span class="n">solution</span> <span class="o">=</span> <span class="n">sympy</span><span class="o">.</span><span class="n">stationary_points</span><span class="p">(</span><span class="n">problem</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
 </span><span id="stationary_points-97"><a href="#stationary_points-97"><span class="linenos">97</span></a>
-</span><span id="stationary_points-98"><a href="#stationary_points-98"><span class="linenos">98</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="s1">&#39;f(x)=&#39;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">problem</span><span class="p">)</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="s1">&#39;**&#39;</span><span class="p">,</span> <span class="s1">&#39;^&#39;</span><span class="p">)</span>
+</span><span id="stationary_points-98"><a href="#stationary_points-98"><span class="linenos">98</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="s1">&#39;f(x)=&#39;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">problem</span><span class="p">)</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="s1">&#39;**&#39;</span><span class="p">,</span> <span class="s1">&#39;^&#39;</span><span class="p">)</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="s1">&#39;*&#39;</span><span class="p">,</span><span class="s1">&#39;&#39;</span><span class="p">)</span>
 </span><span id="stationary_points-99"><a href="#stationary_points-99"><span class="linenos">99</span></a>    <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="n">problem</span><span class="si">}</span><span class="s1">$&#39;</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="n">sympy</span><span class="o">.</span><span class="n">latex</span><span class="p">(</span><span class="n">solution</span><span class="p">)[</span><span class="mi">6</span><span class="p">:</span><span class="o">-</span><span class="mi">8</span><span class="p">]</span><span class="si">}</span><span class="se">}}</span><span class="s1">$&#39;</span>
 </span></pre></div>
 
@@ -426,7 +426,7 @@
 </thead>
 <tbody>
 <tr>
-  <td>$f(x)=6<em>x^3 + 6</em>x^2 + x + 8$</td>
+  <td>$f(x)=6x^3 + 6x^2 + x + 8$</td>
   <td>${- \frac{1}{3} - \frac{\sqrt{2}}{6}, - \frac{1}{3} + \frac{\sqrt{2}}{6}}$</td>
 </tr>
 </tbody>
@@ -447,7 +447,7 @@
     </div>
     <a class="headerlink" href="#trig_differentiation"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="trig_differentiation-102"><a href="#trig_differentiation-102"><span class="linenos">102</span></a><span class="k">def</span> <span class="nf">trig_differentiation</span><span class="p">():</span>
-</span><span id="trig_differentiation-103"><a href="#trig_differentiation-103"><span class="linenos">103</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Trigonometric Differentiation</span>
+</span><span id="trig_differentiation-103"><a href="#trig_differentiation-103"><span class="linenos">103</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Trigonometric Differentiation</span>
 </span><span id="trig_differentiation-104"><a href="#trig_differentiation-104"><span class="linenos">104</span></a>
 </span><span id="trig_differentiation-105"><a href="#trig_differentiation-105"><span class="linenos">105</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="trig_differentiation-106"><a href="#trig_differentiation-106"><span class="linenos">106</span></a><span class="sd">    | --- | --- |</span>
@@ -609,7 +609,7 @@
                         if (doc.annotation)
                             heading += `<span class="annotation">${doc.annotation}</span>`;
                         if (doc.default_value)
-                            heading += `<span class="default_value">${doc.default_value}</span>`;
+                            heading += `<span class="default_value"> = ${doc.default_value}</span>`;
                         break;
                     default:
                         heading = `<span class="name">${doc.fullname}</span>`;
diff --git a/docs/mathgenerator/computer_science.html b/docs/mathgenerator/computer_science.html
index 3fee608..d4d542a 100644
--- a/docs/mathgenerator/computer_science.html
+++ b/docs/mathgenerator/computer_science.html
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@@ -50,8 +50,8 @@
 
 
 
-        <h2>API Documentation</h2>
-            <ul class="memberlist">
+            <h2>API Documentation</h2>
+                <ul class="memberlist">
             <li>
                     <a class="function" href="#bcd_to_decimal">bcd_to_decimal</a>
             </li>
@@ -114,7 +114,7 @@
 </span><span id="L-3"><a href="#L-3"><span class="linenos">  3</span></a>
 </span><span id="L-4"><a href="#L-4"><span class="linenos">  4</span></a>
 </span><span id="L-5"><a href="#L-5"><span class="linenos">  5</span></a><span class="k">def</span> <span class="nf">bcd_to_decimal</span><span class="p">(</span><span class="n">max_number</span><span class="o">=</span><span class="mi">10000</span><span class="p">):</span>
-</span><span id="L-6"><a href="#L-6"><span class="linenos">  6</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Binary Coded Decimal to Integer</span>
+</span><span id="L-6"><a href="#L-6"><span class="linenos">  6</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Binary Coded Decimal to Integer</span>
 </span><span id="L-7"><a href="#L-7"><span class="linenos">  7</span></a>
 </span><span id="L-8"><a href="#L-8"><span class="linenos">  8</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-9"><a href="#L-9"><span class="linenos">  9</span></a><span class="sd">    | --- | --- |</span>
@@ -134,12 +134,12 @@
 </span><span id="L-23"><a href="#L-23"><span class="linenos"> 23</span></a>            <span class="n">n</span> <span class="o">=</span> <span class="n">q</span>
 </span><span id="L-24"><a href="#L-24"><span class="linenos"> 24</span></a>
 </span><span id="L-25"><a href="#L-25"><span class="linenos"> 25</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Integer of Binary Coded Decimal $</span><span class="si">{</span><span class="n">n</span><span class="si">}</span><span class="s2"> =$ &quot;</span>
-</span><span id="L-26"><a href="#L-26"><span class="linenos"> 26</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="nb">int</span><span class="p">(</span><span class="n">binstring</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span><span class="si">}</span><span class="s1">$&#39;</span>
+</span><span id="L-26"><a href="#L-26"><span class="linenos"> 26</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="nb">int</span><span class="p">(</span><span class="n">binstring</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="si">}</span><span class="s1">$&#39;</span>
 </span><span id="L-27"><a href="#L-27"><span class="linenos"> 27</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span><span id="L-28"><a href="#L-28"><span class="linenos"> 28</span></a>
 </span><span id="L-29"><a href="#L-29"><span class="linenos"> 29</span></a>
 </span><span id="L-30"><a href="#L-30"><span class="linenos"> 30</span></a><span class="k">def</span> <span class="nf">binary_2s_complement</span><span class="p">(</span><span class="n">maxDigits</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-31"><a href="#L-31"><span class="linenos"> 31</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Binary 2&#39;s Complement</span>
+</span><span id="L-31"><a href="#L-31"><span class="linenos"> 31</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Binary 2&#39;s Complement</span>
 </span><span id="L-32"><a href="#L-32"><span class="linenos"> 32</span></a>
 </span><span id="L-33"><a href="#L-33"><span class="linenos"> 33</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-34"><a href="#L-34"><span class="linenos"> 34</span></a><span class="sd">    | --- | --- |</span>
@@ -172,7 +172,7 @@
 </span><span id="L-61"><a href="#L-61"><span class="linenos"> 61</span></a>
 </span><span id="L-62"><a href="#L-62"><span class="linenos"> 62</span></a>
 </span><span id="L-63"><a href="#L-63"><span class="linenos"> 63</span></a><span class="k">def</span> <span class="nf">binary_complement_1s</span><span class="p">(</span><span class="n">maxDigits</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-64"><a href="#L-64"><span class="linenos"> 64</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Binary Complement 1s</span>
+</span><span id="L-64"><a href="#L-64"><span class="linenos"> 64</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Binary Complement 1s</span>
 </span><span id="L-65"><a href="#L-65"><span class="linenos"> 65</span></a>
 </span><span id="L-66"><a href="#L-66"><span class="linenos"> 66</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-67"><a href="#L-67"><span class="linenos"> 67</span></a><span class="sd">    | --- | --- |</span>
@@ -187,7 +187,7 @@
 </span><span id="L-76"><a href="#L-76"><span class="linenos"> 76</span></a>
 </span><span id="L-77"><a href="#L-77"><span class="linenos"> 77</span></a>
 </span><span id="L-78"><a href="#L-78"><span class="linenos"> 78</span></a><span class="k">def</span> <span class="nf">binary_to_decimal</span><span class="p">(</span><span class="n">max_dig</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-79"><a href="#L-79"><span class="linenos"> 79</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Binary to Decimal</span>
+</span><span id="L-79"><a href="#L-79"><span class="linenos"> 79</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Binary to Decimal</span>
 </span><span id="L-80"><a href="#L-80"><span class="linenos"> 80</span></a>
 </span><span id="L-81"><a href="#L-81"><span class="linenos"> 81</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-82"><a href="#L-82"><span class="linenos"> 82</span></a><span class="sd">    | --- | --- |</span>
@@ -195,12 +195,12 @@
 </span><span id="L-84"><a href="#L-84"><span class="linenos"> 84</span></a><span class="sd">    &quot;&quot;&quot;</span>
 </span><span id="L-85"><a href="#L-85"><span class="linenos"> 85</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="s1">&#39;&#39;</span><span class="o">.</span><span class="n">join</span><span class="p">([</span><span class="nb">str</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
 </span><span id="L-86"><a href="#L-86"><span class="linenos"> 86</span></a>                      <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_dig</span><span class="p">))])</span>
-</span><span id="L-87"><a href="#L-87"><span class="linenos"> 87</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="nb">int</span><span class="p">(</span><span class="n">problem</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span><span class="si">}</span><span class="s1">$&#39;</span>
+</span><span id="L-87"><a href="#L-87"><span class="linenos"> 87</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="nb">int</span><span class="p">(</span><span class="n">problem</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="si">}</span><span class="s1">$&#39;</span>
 </span><span id="L-88"><a href="#L-88"><span class="linenos"> 88</span></a>    <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="n">problem</span><span class="si">}</span><span class="s1">$&#39;</span><span class="p">,</span> <span class="n">solution</span>
 </span><span id="L-89"><a href="#L-89"><span class="linenos"> 89</span></a>
 </span><span id="L-90"><a href="#L-90"><span class="linenos"> 90</span></a>
 </span><span id="L-91"><a href="#L-91"><span class="linenos"> 91</span></a><span class="k">def</span> <span class="nf">binary_to_hex</span><span class="p">(</span><span class="n">max_dig</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-92"><a href="#L-92"><span class="linenos"> 92</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Binary to Hexidecimal</span>
+</span><span id="L-92"><a href="#L-92"><span class="linenos"> 92</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Binary to Hexidecimal</span>
 </span><span id="L-93"><a href="#L-93"><span class="linenos"> 93</span></a>
 </span><span id="L-94"><a href="#L-94"><span class="linenos"> 94</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-95"><a href="#L-95"><span class="linenos"> 95</span></a><span class="sd">    | --- | --- |</span>
@@ -208,12 +208,12 @@
 </span><span id="L-97"><a href="#L-97"><span class="linenos"> 97</span></a><span class="sd">    &quot;&quot;&quot;</span>
 </span><span id="L-98"><a href="#L-98"><span class="linenos"> 98</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="s1">&#39;&#39;</span><span class="o">.</span><span class="n">join</span><span class="p">([</span><span class="nb">str</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
 </span><span id="L-99"><a href="#L-99"><span class="linenos"> 99</span></a>                      <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_dig</span><span class="p">))])</span>
-</span><span id="L-100"><a href="#L-100"><span class="linenos">100</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="nb">hex</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="n">problem</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span><span class="si">}</span><span class="s1">$&#39;</span>
+</span><span id="L-100"><a href="#L-100"><span class="linenos">100</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="nb">hex</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="n">problem</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">))</span><span class="si">}</span><span class="s1">$&#39;</span>
 </span><span id="L-101"><a href="#L-101"><span class="linenos">101</span></a>    <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="n">problem</span><span class="si">}</span><span class="s1">$&#39;</span><span class="p">,</span> <span class="n">solution</span>
 </span><span id="L-102"><a href="#L-102"><span class="linenos">102</span></a>
 </span><span id="L-103"><a href="#L-103"><span class="linenos">103</span></a>
 </span><span id="L-104"><a href="#L-104"><span class="linenos">104</span></a><span class="k">def</span> <span class="nf">decimal_to_bcd</span><span class="p">(</span><span class="n">max_number</span><span class="o">=</span><span class="mi">10000</span><span class="p">):</span>
-</span><span id="L-105"><a href="#L-105"><span class="linenos">105</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Decimal to Binary Coded Decimal</span>
+</span><span id="L-105"><a href="#L-105"><span class="linenos">105</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Decimal to Binary Coded Decimal</span>
 </span><span id="L-106"><a href="#L-106"><span class="linenos">106</span></a>
 </span><span id="L-107"><a href="#L-107"><span class="linenos">107</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-108"><a href="#L-108"><span class="linenos">108</span></a><span class="sd">    | --- | --- |</span>
@@ -233,7 +233,7 @@
 </span><span id="L-122"><a href="#L-122"><span class="linenos">122</span></a>
 </span><span id="L-123"><a href="#L-123"><span class="linenos">123</span></a>
 </span><span id="L-124"><a href="#L-124"><span class="linenos">124</span></a><span class="k">def</span> <span class="nf">decimal_to_binary</span><span class="p">(</span><span class="n">max_dec</span><span class="o">=</span><span class="mi">99</span><span class="p">):</span>
-</span><span id="L-125"><a href="#L-125"><span class="linenos">125</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Decimal to Binary</span>
+</span><span id="L-125"><a href="#L-125"><span class="linenos">125</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Decimal to Binary</span>
 </span><span id="L-126"><a href="#L-126"><span class="linenos">126</span></a>
 </span><span id="L-127"><a href="#L-127"><span class="linenos">127</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-128"><a href="#L-128"><span class="linenos">128</span></a><span class="sd">    | --- | --- |</span>
@@ -248,7 +248,7 @@
 </span><span id="L-137"><a href="#L-137"><span class="linenos">137</span></a>
 </span><span id="L-138"><a href="#L-138"><span class="linenos">138</span></a>
 </span><span id="L-139"><a href="#L-139"><span class="linenos">139</span></a><span class="k">def</span> <span class="nf">decimal_to_hexadeci</span><span class="p">(</span><span class="n">max_dec</span><span class="o">=</span><span class="mi">1000</span><span class="p">):</span>
-</span><span id="L-140"><a href="#L-140"><span class="linenos">140</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Decimal to Hexadecimal</span>
+</span><span id="L-140"><a href="#L-140"><span class="linenos">140</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Decimal to Hexadecimal</span>
 </span><span id="L-141"><a href="#L-141"><span class="linenos">141</span></a>
 </span><span id="L-142"><a href="#L-142"><span class="linenos">142</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-143"><a href="#L-143"><span class="linenos">143</span></a><span class="sd">    | --- | --- |</span>
@@ -263,7 +263,7 @@
 </span><span id="L-152"><a href="#L-152"><span class="linenos">152</span></a>
 </span><span id="L-153"><a href="#L-153"><span class="linenos">153</span></a>
 </span><span id="L-154"><a href="#L-154"><span class="linenos">154</span></a><span class="k">def</span> <span class="nf">decimal_to_octal</span><span class="p">(</span><span class="n">max_decimal</span><span class="o">=</span><span class="mi">4096</span><span class="p">):</span>
-</span><span id="L-155"><a href="#L-155"><span class="linenos">155</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Decimal to Octal</span>
+</span><span id="L-155"><a href="#L-155"><span class="linenos">155</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Decimal to Octal</span>
 </span><span id="L-156"><a href="#L-156"><span class="linenos">156</span></a>
 </span><span id="L-157"><a href="#L-157"><span class="linenos">157</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-158"><a href="#L-158"><span class="linenos">158</span></a><span class="sd">    | --- | --- |</span>
@@ -278,7 +278,7 @@
 </span><span id="L-167"><a href="#L-167"><span class="linenos">167</span></a>
 </span><span id="L-168"><a href="#L-168"><span class="linenos">168</span></a>
 </span><span id="L-169"><a href="#L-169"><span class="linenos">169</span></a><span class="k">def</span> <span class="nf">fibonacci_series</span><span class="p">(</span><span class="n">min_no</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
-</span><span id="L-170"><a href="#L-170"><span class="linenos">170</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Fibonacci Series</span>
+</span><span id="L-170"><a href="#L-170"><span class="linenos">170</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Fibonacci Series</span>
 </span><span id="L-171"><a href="#L-171"><span class="linenos">171</span></a>
 </span><span id="L-172"><a href="#L-172"><span class="linenos">172</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-173"><a href="#L-173"><span class="linenos">173</span></a><span class="sd">    | --- | --- |</span>
@@ -304,7 +304,7 @@
 </span><span id="L-193"><a href="#L-193"><span class="linenos">193</span></a>
 </span><span id="L-194"><a href="#L-194"><span class="linenos">194</span></a>
 </span><span id="L-195"><a href="#L-195"><span class="linenos">195</span></a><span class="k">def</span> <span class="nf">modulo_division</span><span class="p">(</span><span class="n">max_res</span><span class="o">=</span><span class="mi">99</span><span class="p">,</span> <span class="n">max_modulo</span><span class="o">=</span><span class="mi">99</span><span class="p">):</span>
-</span><span id="L-196"><a href="#L-196"><span class="linenos">196</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Modulo Division</span>
+</span><span id="L-196"><a href="#L-196"><span class="linenos">196</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Modulo Division</span>
 </span><span id="L-197"><a href="#L-197"><span class="linenos">197</span></a>
 </span><span id="L-198"><a href="#L-198"><span class="linenos">198</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-199"><a href="#L-199"><span class="linenos">199</span></a><span class="sd">    | --- | --- |</span>
@@ -320,7 +320,7 @@
 </span><span id="L-209"><a href="#L-209"><span class="linenos">209</span></a>
 </span><span id="L-210"><a href="#L-210"><span class="linenos">210</span></a>
 </span><span id="L-211"><a href="#L-211"><span class="linenos">211</span></a><span class="k">def</span> <span class="nf">nth_fibonacci_number</span><span class="p">(</span><span class="n">max_n</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="L-212"><a href="#L-212"><span class="linenos">212</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;nth Fibonacci number</span>
+</span><span id="L-212"><a href="#L-212"><span class="linenos">212</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;nth Fibonacci number</span>
 </span><span id="L-213"><a href="#L-213"><span class="linenos">213</span></a>
 </span><span id="L-214"><a href="#L-214"><span class="linenos">214</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-215"><a href="#L-215"><span class="linenos">215</span></a><span class="sd">    | --- | --- |</span>
@@ -350,7 +350,7 @@
     </div>
     <a class="headerlink" href="#bcd_to_decimal"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="bcd_to_decimal-6"><a href="#bcd_to_decimal-6"><span class="linenos"> 6</span></a><span class="k">def</span> <span class="nf">bcd_to_decimal</span><span class="p">(</span><span class="n">max_number</span><span class="o">=</span><span class="mi">10000</span><span class="p">):</span>
-</span><span id="bcd_to_decimal-7"><a href="#bcd_to_decimal-7"><span class="linenos"> 7</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Binary Coded Decimal to Integer</span>
+</span><span id="bcd_to_decimal-7"><a href="#bcd_to_decimal-7"><span class="linenos"> 7</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Binary Coded Decimal to Integer</span>
 </span><span id="bcd_to_decimal-8"><a href="#bcd_to_decimal-8"><span class="linenos"> 8</span></a>
 </span><span id="bcd_to_decimal-9"><a href="#bcd_to_decimal-9"><span class="linenos"> 9</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="bcd_to_decimal-10"><a href="#bcd_to_decimal-10"><span class="linenos">10</span></a><span class="sd">    | --- | --- |</span>
@@ -370,7 +370,7 @@
 </span><span id="bcd_to_decimal-24"><a href="#bcd_to_decimal-24"><span class="linenos">24</span></a>            <span class="n">n</span> <span class="o">=</span> <span class="n">q</span>
 </span><span id="bcd_to_decimal-25"><a href="#bcd_to_decimal-25"><span class="linenos">25</span></a>
 </span><span id="bcd_to_decimal-26"><a href="#bcd_to_decimal-26"><span class="linenos">26</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Integer of Binary Coded Decimal $</span><span class="si">{</span><span class="n">n</span><span class="si">}</span><span class="s2"> =$ &quot;</span>
-</span><span id="bcd_to_decimal-27"><a href="#bcd_to_decimal-27"><span class="linenos">27</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="nb">int</span><span class="p">(</span><span class="n">binstring</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span><span class="si">}</span><span class="s1">$&#39;</span>
+</span><span id="bcd_to_decimal-27"><a href="#bcd_to_decimal-27"><span class="linenos">27</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="nb">int</span><span class="p">(</span><span class="n">binstring</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="si">}</span><span class="s1">$&#39;</span>
 </span><span id="bcd_to_decimal-28"><a href="#bcd_to_decimal-28"><span class="linenos">28</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span></pre></div>
 
@@ -407,7 +407,7 @@
     </div>
     <a class="headerlink" href="#binary_2s_complement"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="binary_2s_complement-31"><a href="#binary_2s_complement-31"><span class="linenos">31</span></a><span class="k">def</span> <span class="nf">binary_2s_complement</span><span class="p">(</span><span class="n">maxDigits</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="binary_2s_complement-32"><a href="#binary_2s_complement-32"><span class="linenos">32</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Binary 2&#39;s Complement</span>
+</span><span id="binary_2s_complement-32"><a href="#binary_2s_complement-32"><span class="linenos">32</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Binary 2&#39;s Complement</span>
 </span><span id="binary_2s_complement-33"><a href="#binary_2s_complement-33"><span class="linenos">33</span></a>
 </span><span id="binary_2s_complement-34"><a href="#binary_2s_complement-34"><span class="linenos">34</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="binary_2s_complement-35"><a href="#binary_2s_complement-35"><span class="linenos">35</span></a><span class="sd">    | --- | --- |</span>
@@ -472,7 +472,7 @@
     </div>
     <a class="headerlink" href="#binary_complement_1s"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="binary_complement_1s-64"><a href="#binary_complement_1s-64"><span class="linenos">64</span></a><span class="k">def</span> <span class="nf">binary_complement_1s</span><span class="p">(</span><span class="n">maxDigits</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="binary_complement_1s-65"><a href="#binary_complement_1s-65"><span class="linenos">65</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Binary Complement 1s</span>
+</span><span id="binary_complement_1s-65"><a href="#binary_complement_1s-65"><span class="linenos">65</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Binary Complement 1s</span>
 </span><span id="binary_complement_1s-66"><a href="#binary_complement_1s-66"><span class="linenos">66</span></a>
 </span><span id="binary_complement_1s-67"><a href="#binary_complement_1s-67"><span class="linenos">67</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="binary_complement_1s-68"><a href="#binary_complement_1s-68"><span class="linenos">68</span></a><span class="sd">    | --- | --- |</span>
@@ -519,7 +519,7 @@
     </div>
     <a class="headerlink" href="#binary_to_decimal"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="binary_to_decimal-79"><a href="#binary_to_decimal-79"><span class="linenos">79</span></a><span class="k">def</span> <span class="nf">binary_to_decimal</span><span class="p">(</span><span class="n">max_dig</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="binary_to_decimal-80"><a href="#binary_to_decimal-80"><span class="linenos">80</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Binary to Decimal</span>
+</span><span id="binary_to_decimal-80"><a href="#binary_to_decimal-80"><span class="linenos">80</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Binary to Decimal</span>
 </span><span id="binary_to_decimal-81"><a href="#binary_to_decimal-81"><span class="linenos">81</span></a>
 </span><span id="binary_to_decimal-82"><a href="#binary_to_decimal-82"><span class="linenos">82</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="binary_to_decimal-83"><a href="#binary_to_decimal-83"><span class="linenos">83</span></a><span class="sd">    | --- | --- |</span>
@@ -527,7 +527,7 @@
 </span><span id="binary_to_decimal-85"><a href="#binary_to_decimal-85"><span class="linenos">85</span></a><span class="sd">    &quot;&quot;&quot;</span>
 </span><span id="binary_to_decimal-86"><a href="#binary_to_decimal-86"><span class="linenos">86</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="s1">&#39;&#39;</span><span class="o">.</span><span class="n">join</span><span class="p">([</span><span class="nb">str</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
 </span><span id="binary_to_decimal-87"><a href="#binary_to_decimal-87"><span class="linenos">87</span></a>                      <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_dig</span><span class="p">))])</span>
-</span><span id="binary_to_decimal-88"><a href="#binary_to_decimal-88"><span class="linenos">88</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="nb">int</span><span class="p">(</span><span class="n">problem</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span><span class="si">}</span><span class="s1">$&#39;</span>
+</span><span id="binary_to_decimal-88"><a href="#binary_to_decimal-88"><span class="linenos">88</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="nb">int</span><span class="p">(</span><span class="n">problem</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="si">}</span><span class="s1">$&#39;</span>
 </span><span id="binary_to_decimal-89"><a href="#binary_to_decimal-89"><span class="linenos">89</span></a>    <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="n">problem</span><span class="si">}</span><span class="s1">$&#39;</span><span class="p">,</span> <span class="n">solution</span>
 </span></pre></div>
 
@@ -564,7 +564,7 @@
     </div>
     <a class="headerlink" href="#binary_to_hex"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="binary_to_hex-92"><a href="#binary_to_hex-92"><span class="linenos"> 92</span></a><span class="k">def</span> <span class="nf">binary_to_hex</span><span class="p">(</span><span class="n">max_dig</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="binary_to_hex-93"><a href="#binary_to_hex-93"><span class="linenos"> 93</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Binary to Hexidecimal</span>
+</span><span id="binary_to_hex-93"><a href="#binary_to_hex-93"><span class="linenos"> 93</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Binary to Hexidecimal</span>
 </span><span id="binary_to_hex-94"><a href="#binary_to_hex-94"><span class="linenos"> 94</span></a>
 </span><span id="binary_to_hex-95"><a href="#binary_to_hex-95"><span class="linenos"> 95</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="binary_to_hex-96"><a href="#binary_to_hex-96"><span class="linenos"> 96</span></a><span class="sd">    | --- | --- |</span>
@@ -572,7 +572,7 @@
 </span><span id="binary_to_hex-98"><a href="#binary_to_hex-98"><span class="linenos"> 98</span></a><span class="sd">    &quot;&quot;&quot;</span>
 </span><span id="binary_to_hex-99"><a href="#binary_to_hex-99"><span class="linenos"> 99</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="s1">&#39;&#39;</span><span class="o">.</span><span class="n">join</span><span class="p">([</span><span class="nb">str</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
 </span><span id="binary_to_hex-100"><a href="#binary_to_hex-100"><span class="linenos">100</span></a>                      <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_dig</span><span class="p">))])</span>
-</span><span id="binary_to_hex-101"><a href="#binary_to_hex-101"><span class="linenos">101</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="nb">hex</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="n">problem</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span><span class="si">}</span><span class="s1">$&#39;</span>
+</span><span id="binary_to_hex-101"><a href="#binary_to_hex-101"><span class="linenos">101</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="nb">hex</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="n">problem</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">))</span><span class="si">}</span><span class="s1">$&#39;</span>
 </span><span id="binary_to_hex-102"><a href="#binary_to_hex-102"><span class="linenos">102</span></a>    <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="n">problem</span><span class="si">}</span><span class="s1">$&#39;</span><span class="p">,</span> <span class="n">solution</span>
 </span></pre></div>
 
@@ -609,7 +609,7 @@
     </div>
     <a class="headerlink" href="#decimal_to_bcd"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="decimal_to_bcd-105"><a href="#decimal_to_bcd-105"><span class="linenos">105</span></a><span class="k">def</span> <span class="nf">decimal_to_bcd</span><span class="p">(</span><span class="n">max_number</span><span class="o">=</span><span class="mi">10000</span><span class="p">):</span>
-</span><span id="decimal_to_bcd-106"><a href="#decimal_to_bcd-106"><span class="linenos">106</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Decimal to Binary Coded Decimal</span>
+</span><span id="decimal_to_bcd-106"><a href="#decimal_to_bcd-106"><span class="linenos">106</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Decimal to Binary Coded Decimal</span>
 </span><span id="decimal_to_bcd-107"><a href="#decimal_to_bcd-107"><span class="linenos">107</span></a>
 </span><span id="decimal_to_bcd-108"><a href="#decimal_to_bcd-108"><span class="linenos">108</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="decimal_to_bcd-109"><a href="#decimal_to_bcd-109"><span class="linenos">109</span></a><span class="sd">    | --- | --- |</span>
@@ -661,7 +661,7 @@
     </div>
     <a class="headerlink" href="#decimal_to_binary"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="decimal_to_binary-125"><a href="#decimal_to_binary-125"><span class="linenos">125</span></a><span class="k">def</span> <span class="nf">decimal_to_binary</span><span class="p">(</span><span class="n">max_dec</span><span class="o">=</span><span class="mi">99</span><span class="p">):</span>
-</span><span id="decimal_to_binary-126"><a href="#decimal_to_binary-126"><span class="linenos">126</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Decimal to Binary</span>
+</span><span id="decimal_to_binary-126"><a href="#decimal_to_binary-126"><span class="linenos">126</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Decimal to Binary</span>
 </span><span id="decimal_to_binary-127"><a href="#decimal_to_binary-127"><span class="linenos">127</span></a>
 </span><span id="decimal_to_binary-128"><a href="#decimal_to_binary-128"><span class="linenos">128</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="decimal_to_binary-129"><a href="#decimal_to_binary-129"><span class="linenos">129</span></a><span class="sd">    | --- | --- |</span>
@@ -708,7 +708,7 @@
     </div>
     <a class="headerlink" href="#decimal_to_hexadeci"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="decimal_to_hexadeci-140"><a href="#decimal_to_hexadeci-140"><span class="linenos">140</span></a><span class="k">def</span> <span class="nf">decimal_to_hexadeci</span><span class="p">(</span><span class="n">max_dec</span><span class="o">=</span><span class="mi">1000</span><span class="p">):</span>
-</span><span id="decimal_to_hexadeci-141"><a href="#decimal_to_hexadeci-141"><span class="linenos">141</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Decimal to Hexadecimal</span>
+</span><span id="decimal_to_hexadeci-141"><a href="#decimal_to_hexadeci-141"><span class="linenos">141</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Decimal to Hexadecimal</span>
 </span><span id="decimal_to_hexadeci-142"><a href="#decimal_to_hexadeci-142"><span class="linenos">142</span></a>
 </span><span id="decimal_to_hexadeci-143"><a href="#decimal_to_hexadeci-143"><span class="linenos">143</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="decimal_to_hexadeci-144"><a href="#decimal_to_hexadeci-144"><span class="linenos">144</span></a><span class="sd">    | --- | --- |</span>
@@ -755,7 +755,7 @@
     </div>
     <a class="headerlink" href="#decimal_to_octal"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="decimal_to_octal-155"><a href="#decimal_to_octal-155"><span class="linenos">155</span></a><span class="k">def</span> <span class="nf">decimal_to_octal</span><span class="p">(</span><span class="n">max_decimal</span><span class="o">=</span><span class="mi">4096</span><span class="p">):</span>
-</span><span id="decimal_to_octal-156"><a href="#decimal_to_octal-156"><span class="linenos">156</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Decimal to Octal</span>
+</span><span id="decimal_to_octal-156"><a href="#decimal_to_octal-156"><span class="linenos">156</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Decimal to Octal</span>
 </span><span id="decimal_to_octal-157"><a href="#decimal_to_octal-157"><span class="linenos">157</span></a>
 </span><span id="decimal_to_octal-158"><a href="#decimal_to_octal-158"><span class="linenos">158</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="decimal_to_octal-159"><a href="#decimal_to_octal-159"><span class="linenos">159</span></a><span class="sd">    | --- | --- |</span>
@@ -802,7 +802,7 @@
     </div>
     <a class="headerlink" href="#fibonacci_series"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="fibonacci_series-170"><a href="#fibonacci_series-170"><span class="linenos">170</span></a><span class="k">def</span> <span class="nf">fibonacci_series</span><span class="p">(</span><span class="n">min_no</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
-</span><span id="fibonacci_series-171"><a href="#fibonacci_series-171"><span class="linenos">171</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Fibonacci Series</span>
+</span><span id="fibonacci_series-171"><a href="#fibonacci_series-171"><span class="linenos">171</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Fibonacci Series</span>
 </span><span id="fibonacci_series-172"><a href="#fibonacci_series-172"><span class="linenos">172</span></a>
 </span><span id="fibonacci_series-173"><a href="#fibonacci_series-173"><span class="linenos">173</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="fibonacci_series-174"><a href="#fibonacci_series-174"><span class="linenos">174</span></a><span class="sd">    | --- | --- |</span>
@@ -860,7 +860,7 @@
     </div>
     <a class="headerlink" href="#modulo_division"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="modulo_division-196"><a href="#modulo_division-196"><span class="linenos">196</span></a><span class="k">def</span> <span class="nf">modulo_division</span><span class="p">(</span><span class="n">max_res</span><span class="o">=</span><span class="mi">99</span><span class="p">,</span> <span class="n">max_modulo</span><span class="o">=</span><span class="mi">99</span><span class="p">):</span>
-</span><span id="modulo_division-197"><a href="#modulo_division-197"><span class="linenos">197</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Modulo Division</span>
+</span><span id="modulo_division-197"><a href="#modulo_division-197"><span class="linenos">197</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Modulo Division</span>
 </span><span id="modulo_division-198"><a href="#modulo_division-198"><span class="linenos">198</span></a>
 </span><span id="modulo_division-199"><a href="#modulo_division-199"><span class="linenos">199</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="modulo_division-200"><a href="#modulo_division-200"><span class="linenos">200</span></a><span class="sd">    | --- | --- |</span>
@@ -908,7 +908,7 @@
     </div>
     <a class="headerlink" href="#nth_fibonacci_number"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="nth_fibonacci_number-212"><a href="#nth_fibonacci_number-212"><span class="linenos">212</span></a><span class="k">def</span> <span class="nf">nth_fibonacci_number</span><span class="p">(</span><span class="n">max_n</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="nth_fibonacci_number-213"><a href="#nth_fibonacci_number-213"><span class="linenos">213</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;nth Fibonacci number</span>
+</span><span id="nth_fibonacci_number-213"><a href="#nth_fibonacci_number-213"><span class="linenos">213</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;nth Fibonacci number</span>
 </span><span id="nth_fibonacci_number-214"><a href="#nth_fibonacci_number-214"><span class="linenos">214</span></a>
 </span><span id="nth_fibonacci_number-215"><a href="#nth_fibonacci_number-215"><span class="linenos">215</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="nth_fibonacci_number-216"><a href="#nth_fibonacci_number-216"><span class="linenos">216</span></a><span class="sd">    | --- | --- |</span>
@@ -1065,7 +1065,7 @@
                         if (doc.annotation)
                             heading += `<span class="annotation">${doc.annotation}</span>`;
                         if (doc.default_value)
-                            heading += `<span class="default_value">${doc.default_value}</span>`;
+                            heading += `<span class="default_value"> = ${doc.default_value}</span>`;
                         break;
                     default:
                         heading = `<span class="name">${doc.fullname}</span>`;
diff --git a/docs/mathgenerator/geometry.html b/docs/mathgenerator/geometry.html
index dc4377b..d4c0a63 100644
--- a/docs/mathgenerator/geometry.html
+++ b/docs/mathgenerator/geometry.html
@@ -3,14 +3,14 @@
 <head>
     <meta charset="utf-8">
     <meta name="viewport" content="width=device-width, initial-scale=1">
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@@ -50,8 +50,8 @@
 
 
 
-        <h2>API Documentation</h2>
-            <ul class="memberlist">
+            <h2>API Documentation</h2>
+                <ul class="memberlist">
             <li>
                     <a class="function" href="#angle_btw_vectors">angle_btw_vectors</a>
             </li>
@@ -181,7 +181,7 @@
 </span><span id="L-4"><a href="#L-4"><span class="linenos">  4</span></a>
 </span><span id="L-5"><a href="#L-5"><span class="linenos">  5</span></a>
 </span><span id="L-6"><a href="#L-6"><span class="linenos">  6</span></a><span class="k">def</span> <span class="nf">angle_btw_vectors</span><span class="p">(</span><span class="n">max_elt_amt</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="L-7"><a href="#L-7"><span class="linenos">  7</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Angle between 2 vectors</span>
+</span><span id="L-7"><a href="#L-7"><span class="linenos">  7</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Angle between 2 vectors</span>
 </span><span id="L-8"><a href="#L-8"><span class="linenos">  8</span></a>
 </span><span id="L-9"><a href="#L-9"><span class="linenos">  9</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-10"><a href="#L-10"><span class="linenos"> 10</span></a><span class="sd">    | --- | --- |</span>
@@ -213,7 +213,7 @@
 </span><span id="L-36"><a href="#L-36"><span class="linenos"> 36</span></a>
 </span><span id="L-37"><a href="#L-37"><span class="linenos"> 37</span></a>
 </span><span id="L-38"><a href="#L-38"><span class="linenos"> 38</span></a><span class="k">def</span> <span class="nf">angle_regular_polygon</span><span class="p">(</span><span class="n">min_val</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">max_val</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="L-39"><a href="#L-39"><span class="linenos"> 39</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Angle of a Regular Polygon</span>
+</span><span id="L-39"><a href="#L-39"><span class="linenos"> 39</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Angle of a Regular Polygon</span>
 </span><span id="L-40"><a href="#L-40"><span class="linenos"> 40</span></a>
 </span><span id="L-41"><a href="#L-41"><span class="linenos"> 41</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-42"><a href="#L-42"><span class="linenos"> 42</span></a><span class="sd">    | --- | --- |</span>
@@ -223,13 +223,13 @@
 </span><span id="L-46"><a href="#L-46"><span class="linenos"> 46</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Find the angle of a regular polygon with $</span><span class="si">{</span><span class="n">sideNum</span><span class="si">}</span><span class="s2">$ sides&quot;</span>
 </span><span id="L-47"><a href="#L-47"><span class="linenos"> 47</span></a>
 </span><span id="L-48"><a href="#L-48"><span class="linenos"> 48</span></a>    <span class="n">exteriorAngle</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="mi">360</span> <span class="o">/</span> <span class="n">sideNum</span><span class="p">),</span> <span class="mi">2</span><span class="p">)</span>
-</span><span id="L-49"><a href="#L-49"><span class="linenos"> 49</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="mi">180</span> <span class="o">-</span> <span class="n">exteriorAngle</span><span class="si">}</span><span class="s1">$&#39;</span>
+</span><span id="L-49"><a href="#L-49"><span class="linenos"> 49</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="mi">180</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">exteriorAngle</span><span class="si">}</span><span class="s1">$&#39;</span>
 </span><span id="L-50"><a href="#L-50"><span class="linenos"> 50</span></a>
 </span><span id="L-51"><a href="#L-51"><span class="linenos"> 51</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span><span id="L-52"><a href="#L-52"><span class="linenos"> 52</span></a>
 </span><span id="L-53"><a href="#L-53"><span class="linenos"> 53</span></a>
 </span><span id="L-54"><a href="#L-54"><span class="linenos"> 54</span></a><span class="k">def</span> <span class="nf">arc_length</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">49</span><span class="p">,</span> <span class="n">max_angle</span><span class="o">=</span><span class="mi">359</span><span class="p">):</span>
-</span><span id="L-55"><a href="#L-55"><span class="linenos"> 55</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Arc length of Angle</span>
+</span><span id="L-55"><a href="#L-55"><span class="linenos"> 55</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Arc length of Angle</span>
 </span><span id="L-56"><a href="#L-56"><span class="linenos"> 56</span></a>
 </span><span id="L-57"><a href="#L-57"><span class="linenos"> 57</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-58"><a href="#L-58"><span class="linenos"> 58</span></a><span class="sd">    | --- | --- |</span>
@@ -246,7 +246,7 @@
 </span><span id="L-69"><a href="#L-69"><span class="linenos"> 69</span></a>
 </span><span id="L-70"><a href="#L-70"><span class="linenos"> 70</span></a>
 </span><span id="L-71"><a href="#L-71"><span class="linenos"> 71</span></a><span class="k">def</span> <span class="nf">area_of_circle</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="L-72"><a href="#L-72"><span class="linenos"> 72</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Area of Circle</span>
+</span><span id="L-72"><a href="#L-72"><span class="linenos"> 72</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Area of Circle</span>
 </span><span id="L-73"><a href="#L-73"><span class="linenos"> 73</span></a>
 </span><span id="L-74"><a href="#L-74"><span class="linenos"> 74</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-75"><a href="#L-75"><span class="linenos"> 75</span></a><span class="sd">    | --- | --- |</span>
@@ -260,7 +260,7 @@
 </span><span id="L-83"><a href="#L-83"><span class="linenos"> 83</span></a>
 </span><span id="L-84"><a href="#L-84"><span class="linenos"> 84</span></a>
 </span><span id="L-85"><a href="#L-85"><span class="linenos"> 85</span></a><span class="k">def</span> <span class="nf">area_of_circle_given_center_and_point</span><span class="p">(</span><span class="n">max_coordinate</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">max_radius</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-86"><a href="#L-86"><span class="linenos"> 86</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Area of Circle given center and a point on circle</span>
+</span><span id="L-86"><a href="#L-86"><span class="linenos"> 86</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Area of Circle given center and a point on circle</span>
 </span><span id="L-87"><a href="#L-87"><span class="linenos"> 87</span></a>
 </span><span id="L-88"><a href="#L-88"><span class="linenos"> 88</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-89"><a href="#L-89"><span class="linenos"> 89</span></a><span class="sd">    | --- | --- |</span>
@@ -282,7 +282,7 @@
 </span><span id="L-105"><a href="#L-105"><span class="linenos">105</span></a>
 </span><span id="L-106"><a href="#L-106"><span class="linenos">106</span></a>
 </span><span id="L-107"><a href="#L-107"><span class="linenos">107</span></a><span class="k">def</span> <span class="nf">area_of_triangle</span><span class="p">(</span><span class="n">max_a</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_b</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="L-108"><a href="#L-108"><span class="linenos">108</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Area of Triangle</span>
+</span><span id="L-108"><a href="#L-108"><span class="linenos">108</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Area of Triangle</span>
 </span><span id="L-109"><a href="#L-109"><span class="linenos">109</span></a>
 </span><span id="L-110"><a href="#L-110"><span class="linenos">110</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-111"><a href="#L-111"><span class="linenos">111</span></a><span class="sd">    | --- | --- |</span>
@@ -296,14 +296,14 @@
 </span><span id="L-119"><a href="#L-119"><span class="linenos">119</span></a>    <span class="n">area</span> <span class="o">=</span> <span class="p">(</span><span class="n">s</span> <span class="o">*</span> <span class="p">(</span><span class="n">s</span> <span class="o">-</span> <span class="n">a</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">s</span> <span class="o">-</span> <span class="n">b</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">s</span> <span class="o">-</span> <span class="n">c</span><span class="p">))</span><span class="o">**</span><span class="mf">0.5</span>
 </span><span id="L-120"><a href="#L-120"><span class="linenos">120</span></a>
 </span><span id="L-121"><a href="#L-121"><span class="linenos">121</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Area of triangle with side lengths: $</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="s2">, </span><span class="si">{</span><span class="n">b</span><span class="si">}</span><span class="s2">, </span><span class="si">{</span><span class="n">c</span><span class="si">}</span><span class="s2"> = $&quot;</span>
-</span><span id="L-122"><a href="#L-122"><span class="linenos">122</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="nb">round</span><span class="p">(</span><span class="n">area</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span><span class="si">}</span><span class="s1">$&#39;</span>
+</span><span id="L-122"><a href="#L-122"><span class="linenos">122</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="nb">round</span><span class="p">(</span><span class="n">area</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="si">}</span><span class="s1">$&#39;</span>
 </span><span id="L-123"><a href="#L-123"><span class="linenos">123</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span><span id="L-124"><a href="#L-124"><span class="linenos">124</span></a>
 </span><span id="L-125"><a href="#L-125"><span class="linenos">125</span></a>
 </span><span id="L-126"><a href="#L-126"><span class="linenos">126</span></a><span class="c1"># Handles degrees in quadrant one</span>
 </span><span id="L-127"><a href="#L-127"><span class="linenos">127</span></a><span class="k">def</span> <span class="nf">basic_trigonometry</span><span class="p">(</span><span class="n">angles</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">30</span><span class="p">,</span> <span class="mi">45</span><span class="p">,</span> <span class="mi">60</span><span class="p">,</span> <span class="mi">90</span><span class="p">],</span>
 </span><span id="L-128"><a href="#L-128"><span class="linenos">128</span></a>                       <span class="n">functions</span><span class="o">=</span><span class="p">[</span><span class="s2">&quot;sin&quot;</span><span class="p">,</span> <span class="s2">&quot;cos&quot;</span><span class="p">,</span> <span class="s2">&quot;tan&quot;</span><span class="p">]):</span>
-</span><span id="L-129"><a href="#L-129"><span class="linenos">129</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Trigonometric Values</span>
+</span><span id="L-129"><a href="#L-129"><span class="linenos">129</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Trigonometric Values</span>
 </span><span id="L-130"><a href="#L-130"><span class="linenos">130</span></a>
 </span><span id="L-131"><a href="#L-131"><span class="linenos">131</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-132"><a href="#L-132"><span class="linenos">132</span></a><span class="sd">    | --- | --- |</span>
@@ -332,7 +332,7 @@
 </span><span id="L-155"><a href="#L-155"><span class="linenos">155</span></a>
 </span><span id="L-156"><a href="#L-156"><span class="linenos">156</span></a>
 </span><span id="L-157"><a href="#L-157"><span class="linenos">157</span></a><span class="k">def</span> <span class="nf">circumference</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="L-158"><a href="#L-158"><span class="linenos">158</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Circumference of Circle</span>
+</span><span id="L-158"><a href="#L-158"><span class="linenos">158</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Circumference of Circle</span>
 </span><span id="L-159"><a href="#L-159"><span class="linenos">159</span></a>
 </span><span id="L-160"><a href="#L-160"><span class="linenos">160</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-161"><a href="#L-161"><span class="linenos">161</span></a><span class="sd">    | --- | --- |</span>
@@ -346,7 +346,7 @@
 </span><span id="L-169"><a href="#L-169"><span class="linenos">169</span></a>
 </span><span id="L-170"><a href="#L-170"><span class="linenos">170</span></a>
 </span><span id="L-171"><a href="#L-171"><span class="linenos">171</span></a><span class="k">def</span> <span class="nf">complementary_and_supplementary_angle</span><span class="p">(</span><span class="n">max_supp</span><span class="o">=</span><span class="mi">180</span><span class="p">,</span> <span class="n">max_comp</span><span class="o">=</span><span class="mi">90</span><span class="p">):</span>
-</span><span id="L-172"><a href="#L-172"><span class="linenos">172</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Complementary and Supplementary Angle</span>
+</span><span id="L-172"><a href="#L-172"><span class="linenos">172</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Complementary and Supplementary Angle</span>
 </span><span id="L-173"><a href="#L-173"><span class="linenos">173</span></a>
 </span><span id="L-174"><a href="#L-174"><span class="linenos">174</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-175"><a href="#L-175"><span class="linenos">175</span></a><span class="sd">    | --- | --- |</span>
@@ -367,7 +367,7 @@
 </span><span id="L-190"><a href="#L-190"><span class="linenos">190</span></a>
 </span><span id="L-191"><a href="#L-191"><span class="linenos">191</span></a>
 </span><span id="L-192"><a href="#L-192"><span class="linenos">192</span></a><span class="k">def</span> <span class="nf">curved_surface_area_cylinder</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">49</span><span class="p">,</span> <span class="n">max_height</span><span class="o">=</span><span class="mi">99</span><span class="p">):</span>
-</span><span id="L-193"><a href="#L-193"><span class="linenos">193</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Curved surface area of a cylinder</span>
+</span><span id="L-193"><a href="#L-193"><span class="linenos">193</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Curved surface area of a cylinder</span>
 </span><span id="L-194"><a href="#L-194"><span class="linenos">194</span></a>
 </span><span id="L-195"><a href="#L-195"><span class="linenos">195</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-196"><a href="#L-196"><span class="linenos">196</span></a><span class="sd">    | --- | --- |</span>
@@ -384,7 +384,7 @@
 </span><span id="L-207"><a href="#L-207"><span class="linenos">207</span></a>
 </span><span id="L-208"><a href="#L-208"><span class="linenos">208</span></a>
 </span><span id="L-209"><a href="#L-209"><span class="linenos">209</span></a><span class="k">def</span> <span class="nf">degree_to_rad</span><span class="p">(</span><span class="n">max_deg</span><span class="o">=</span><span class="mi">360</span><span class="p">):</span>
-</span><span id="L-210"><a href="#L-210"><span class="linenos">210</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Degrees to Radians</span>
+</span><span id="L-210"><a href="#L-210"><span class="linenos">210</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Degrees to Radians</span>
 </span><span id="L-211"><a href="#L-211"><span class="linenos">211</span></a>
 </span><span id="L-212"><a href="#L-212"><span class="linenos">212</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-213"><a href="#L-213"><span class="linenos">213</span></a><span class="sd">    | --- | --- |</span>
@@ -400,7 +400,7 @@
 </span><span id="L-223"><a href="#L-223"><span class="linenos">223</span></a>
 </span><span id="L-224"><a href="#L-224"><span class="linenos">224</span></a>
 </span><span id="L-225"><a href="#L-225"><span class="linenos">225</span></a><span class="k">def</span> <span class="nf">equation_of_line_from_two_points</span><span class="p">(</span><span class="n">max_coordinate</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">min_coordinate</span><span class="o">=-</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="L-226"><a href="#L-226"><span class="linenos">226</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Equation of line from two points</span>
+</span><span id="L-226"><a href="#L-226"><span class="linenos">226</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Equation of line from two points</span>
 </span><span id="L-227"><a href="#L-227"><span class="linenos">227</span></a>
 </span><span id="L-228"><a href="#L-228"><span class="linenos">228</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-229"><a href="#L-229"><span class="linenos">229</span></a><span class="sd">    | --- | --- |</span>
@@ -462,7 +462,7 @@
 </span><span id="L-285"><a href="#L-285"><span class="linenos">285</span></a>
 </span><span id="L-286"><a href="#L-286"><span class="linenos">286</span></a>
 </span><span id="L-287"><a href="#L-287"><span class="linenos">287</span></a><span class="k">def</span> <span class="nf">fourth_angle_of_quadrilateral</span><span class="p">(</span><span class="n">max_angle</span><span class="o">=</span><span class="mi">180</span><span class="p">):</span>
-</span><span id="L-288"><a href="#L-288"><span class="linenos">288</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Fourth Angle of Quadrilateral</span>
+</span><span id="L-288"><a href="#L-288"><span class="linenos">288</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Fourth Angle of Quadrilateral</span>
 </span><span id="L-289"><a href="#L-289"><span class="linenos">289</span></a>
 </span><span id="L-290"><a href="#L-290"><span class="linenos">290</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-291"><a href="#L-291"><span class="linenos">291</span></a><span class="sd">    | --- | --- |</span>
@@ -481,7 +481,7 @@
 </span><span id="L-304"><a href="#L-304"><span class="linenos">304</span></a>
 </span><span id="L-305"><a href="#L-305"><span class="linenos">305</span></a>
 </span><span id="L-306"><a href="#L-306"><span class="linenos">306</span></a><span class="k">def</span> <span class="nf">perimeter_of_polygons</span><span class="p">(</span><span class="n">max_sides</span><span class="o">=</span><span class="mi">12</span><span class="p">,</span> <span class="n">max_length</span><span class="o">=</span><span class="mi">120</span><span class="p">):</span>
-</span><span id="L-307"><a href="#L-307"><span class="linenos">307</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Perimeter of Polygons</span>
+</span><span id="L-307"><a href="#L-307"><span class="linenos">307</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Perimeter of Polygons</span>
 </span><span id="L-308"><a href="#L-308"><span class="linenos">308</span></a>
 </span><span id="L-309"><a href="#L-309"><span class="linenos">309</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-310"><a href="#L-310"><span class="linenos">310</span></a><span class="sd">    | --- | --- |</span>
@@ -490,14 +490,14 @@
 </span><span id="L-313"><a href="#L-313"><span class="linenos">313</span></a>    <span class="n">size_of_sides</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">max_sides</span><span class="p">)</span>
 </span><span id="L-314"><a href="#L-314"><span class="linenos">314</span></a>    <span class="n">sides</span> <span class="o">=</span> <span class="p">[</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_length</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">size_of_sides</span><span class="p">)]</span>
 </span><span id="L-315"><a href="#L-315"><span class="linenos">315</span></a>
-</span><span id="L-316"><a href="#L-316"><span class="linenos">316</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;The perimeter of a $</span><span class="si">{</span><span class="n">size_of_sides</span><span class="si">}</span><span class="s2">$ sided polygon with lengths of $</span><span class="si">{</span><span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="n">sides</span><span class="p">))</span><span class="si">}</span><span class="s2">$cm is: &quot;</span>
+</span><span id="L-316"><a href="#L-316"><span class="linenos">316</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;The perimeter of a $</span><span class="si">{</span><span class="n">size_of_sides</span><span class="si">}</span><span class="s2">$ sided polygon with lengths of $</span><span class="si">{</span><span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span><span class="w"> </span><span class="n">sides</span><span class="p">))</span><span class="si">}</span><span class="s2">$cm is: &quot;</span>
 </span><span id="L-317"><a href="#L-317"><span class="linenos">317</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">sides</span><span class="p">)</span>
 </span><span id="L-318"><a href="#L-318"><span class="linenos">318</span></a>
 </span><span id="L-319"><a href="#L-319"><span class="linenos">319</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="n">solution</span><span class="si">}</span><span class="s1">$&#39;</span>
 </span><span id="L-320"><a href="#L-320"><span class="linenos">320</span></a>
 </span><span id="L-321"><a href="#L-321"><span class="linenos">321</span></a>
 </span><span id="L-322"><a href="#L-322"><span class="linenos">322</span></a><span class="k">def</span> <span class="nf">pythagorean_theorem</span><span class="p">(</span><span class="n">max_length</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="L-323"><a href="#L-323"><span class="linenos">323</span></a>    <span class="sd">&quot;&quot;&quot;Pythagorean Theorem</span>
+</span><span id="L-323"><a href="#L-323"><span class="linenos">323</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Pythagorean Theorem</span>
 </span><span id="L-324"><a href="#L-324"><span class="linenos">324</span></a>
 </span><span id="L-325"><a href="#L-325"><span class="linenos">325</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-326"><a href="#L-326"><span class="linenos">326</span></a><span class="sd">    | --- | --- |</span>
@@ -513,7 +513,7 @@
 </span><span id="L-336"><a href="#L-336"><span class="linenos">336</span></a>
 </span><span id="L-337"><a href="#L-337"><span class="linenos">337</span></a>
 </span><span id="L-338"><a href="#L-338"><span class="linenos">338</span></a><span class="k">def</span> <span class="nf">radian_to_deg</span><span class="p">(</span><span class="n">max_rad</span><span class="o">=</span><span class="mf">6.28</span><span class="p">):</span>
-</span><span id="L-339"><a href="#L-339"><span class="linenos">339</span></a>    <span class="sd">&quot;&quot;&quot;Radians to Degrees&quot;&quot;&quot;</span>
+</span><span id="L-339"><a href="#L-339"><span class="linenos">339</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Radians to Degrees&quot;&quot;&quot;</span>
 </span><span id="L-340"><a href="#L-340"><span class="linenos">340</span></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">int</span><span class="p">(</span><span class="n">max_rad</span> <span class="o">*</span> <span class="mi">100</span><span class="p">))</span> <span class="o">/</span> <span class="mi">100</span>
 </span><span id="L-341"><a href="#L-341"><span class="linenos">341</span></a>    <span class="n">b</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="mi">180</span> <span class="o">*</span> <span class="n">a</span><span class="p">)</span> <span class="o">/</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
 </span><span id="L-342"><a href="#L-342"><span class="linenos">342</span></a>
@@ -523,7 +523,7 @@
 </span><span id="L-346"><a href="#L-346"><span class="linenos">346</span></a>
 </span><span id="L-347"><a href="#L-347"><span class="linenos">347</span></a>
 </span><span id="L-348"><a href="#L-348"><span class="linenos">348</span></a><span class="k">def</span> <span class="nf">sector_area</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">49</span><span class="p">,</span> <span class="n">max_angle</span><span class="o">=</span><span class="mi">359</span><span class="p">):</span>
-</span><span id="L-349"><a href="#L-349"><span class="linenos">349</span></a>    <span class="sd">&quot;&quot;&quot;Area of a Sector</span>
+</span><span id="L-349"><a href="#L-349"><span class="linenos">349</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Area of a Sector</span>
 </span><span id="L-350"><a href="#L-350"><span class="linenos">350</span></a>
 </span><span id="L-351"><a href="#L-351"><span class="linenos">351</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-352"><a href="#L-352"><span class="linenos">352</span></a><span class="sd">    | --- | --- |</span>
@@ -540,7 +540,7 @@
 </span><span id="L-363"><a href="#L-363"><span class="linenos">363</span></a>
 </span><span id="L-364"><a href="#L-364"><span class="linenos">364</span></a>
 </span><span id="L-365"><a href="#L-365"><span class="linenos">365</span></a><span class="k">def</span> <span class="nf">sum_of_polygon_angles</span><span class="p">(</span><span class="n">max_sides</span><span class="o">=</span><span class="mi">12</span><span class="p">):</span>
-</span><span id="L-366"><a href="#L-366"><span class="linenos">366</span></a>    <span class="sd">&quot;&quot;&quot;Sum of Angles of Polygon</span>
+</span><span id="L-366"><a href="#L-366"><span class="linenos">366</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Sum of Angles of Polygon</span>
 </span><span id="L-367"><a href="#L-367"><span class="linenos">367</span></a>
 </span><span id="L-368"><a href="#L-368"><span class="linenos">368</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-369"><a href="#L-369"><span class="linenos">369</span></a><span class="sd">    | --- | --- |</span>
@@ -554,7 +554,7 @@
 </span><span id="L-377"><a href="#L-377"><span class="linenos">377</span></a>
 </span><span id="L-378"><a href="#L-378"><span class="linenos">378</span></a>
 </span><span id="L-379"><a href="#L-379"><span class="linenos">379</span></a><span class="k">def</span> <span class="nf">surface_area_cone</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_height</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="L-380"><a href="#L-380"><span class="linenos">380</span></a>    <span class="sd">&quot;&quot;&quot;Surface area of a cone</span>
+</span><span id="L-380"><a href="#L-380"><span class="linenos">380</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Surface area of a cone</span>
 </span><span id="L-381"><a href="#L-381"><span class="linenos">381</span></a>
 </span><span id="L-382"><a href="#L-382"><span class="linenos">382</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-383"><a href="#L-383"><span class="linenos">383</span></a><span class="sd">    | --- | --- |</span>
@@ -572,7 +572,7 @@
 </span><span id="L-395"><a href="#L-395"><span class="linenos">395</span></a>
 </span><span id="L-396"><a href="#L-396"><span class="linenos">396</span></a>
 </span><span id="L-397"><a href="#L-397"><span class="linenos">397</span></a><span class="k">def</span> <span class="nf">surface_area_cube</span><span class="p">(</span><span class="n">max_side</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="L-398"><a href="#L-398"><span class="linenos">398</span></a>    <span class="sd">&quot;&quot;&quot;Surface area of a cube</span>
+</span><span id="L-398"><a href="#L-398"><span class="linenos">398</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Surface area of a cube</span>
 </span><span id="L-399"><a href="#L-399"><span class="linenos">399</span></a>
 </span><span id="L-400"><a href="#L-400"><span class="linenos">400</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-401"><a href="#L-401"><span class="linenos">401</span></a><span class="sd">    | --- | --- |</span>
@@ -587,7 +587,7 @@
 </span><span id="L-410"><a href="#L-410"><span class="linenos">410</span></a>
 </span><span id="L-411"><a href="#L-411"><span class="linenos">411</span></a>
 </span><span id="L-412"><a href="#L-412"><span class="linenos">412</span></a><span class="k">def</span> <span class="nf">surface_area_cuboid</span><span class="p">(</span><span class="n">max_side</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="L-413"><a href="#L-413"><span class="linenos">413</span></a>    <span class="sd">&quot;&quot;&quot;Surface area of a cuboid</span>
+</span><span id="L-413"><a href="#L-413"><span class="linenos">413</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Surface area of a cuboid</span>
 </span><span id="L-414"><a href="#L-414"><span class="linenos">414</span></a>
 </span><span id="L-415"><a href="#L-415"><span class="linenos">415</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-416"><a href="#L-416"><span class="linenos">416</span></a><span class="sd">    | --- | --- |</span>
@@ -604,7 +604,7 @@
 </span><span id="L-427"><a href="#L-427"><span class="linenos">427</span></a>
 </span><span id="L-428"><a href="#L-428"><span class="linenos">428</span></a>
 </span><span id="L-429"><a href="#L-429"><span class="linenos">429</span></a><span class="k">def</span> <span class="nf">surface_area_cylinder</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_height</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="L-430"><a href="#L-430"><span class="linenos">430</span></a>    <span class="sd">&quot;&quot;&quot;Surface area of a cylinder</span>
+</span><span id="L-430"><a href="#L-430"><span class="linenos">430</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Surface area of a cylinder</span>
 </span><span id="L-431"><a href="#L-431"><span class="linenos">431</span></a>
 </span><span id="L-432"><a href="#L-432"><span class="linenos">432</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-433"><a href="#L-433"><span class="linenos">433</span></a><span class="sd">    | --- | --- |</span>
@@ -620,7 +620,7 @@
 </span><span id="L-443"><a href="#L-443"><span class="linenos">443</span></a>
 </span><span id="L-444"><a href="#L-444"><span class="linenos">444</span></a>
 </span><span id="L-445"><a href="#L-445"><span class="linenos">445</span></a><span class="k">def</span> <span class="nf">surface_area_pyramid</span><span class="p">(</span><span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="L-446"><a href="#L-446"><span class="linenos">446</span></a>    <span class="sd">&quot;&quot;&quot;Surface area of a pyramid</span>
+</span><span id="L-446"><a href="#L-446"><span class="linenos">446</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Surface area of a pyramid</span>
 </span><span id="L-447"><a href="#L-447"><span class="linenos">447</span></a>
 </span><span id="L-448"><a href="#L-448"><span class="linenos">448</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-449"><a href="#L-449"><span class="linenos">449</span></a><span class="sd">    | --- | --- |</span>
@@ -662,7 +662,7 @@
 </span><span id="L-485"><a href="#L-485"><span class="linenos">485</span></a>
 </span><span id="L-486"><a href="#L-486"><span class="linenos">486</span></a>
 </span><span id="L-487"><a href="#L-487"><span class="linenos">487</span></a><span class="k">def</span> <span class="nf">surface_area_sphere</span><span class="p">(</span><span class="n">max_side</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="L-488"><a href="#L-488"><span class="linenos">488</span></a>    <span class="sd">&quot;&quot;&quot;Surface area of a sphere</span>
+</span><span id="L-488"><a href="#L-488"><span class="linenos">488</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Surface area of a sphere</span>
 </span><span id="L-489"><a href="#L-489"><span class="linenos">489</span></a>
 </span><span id="L-490"><a href="#L-490"><span class="linenos">490</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-491"><a href="#L-491"><span class="linenos">491</span></a><span class="sd">    | --- | --- |</span>
@@ -677,7 +677,7 @@
 </span><span id="L-500"><a href="#L-500"><span class="linenos">500</span></a>
 </span><span id="L-501"><a href="#L-501"><span class="linenos">501</span></a>
 </span><span id="L-502"><a href="#L-502"><span class="linenos">502</span></a><span class="k">def</span> <span class="nf">third_angle_of_triangle</span><span class="p">(</span><span class="n">max_angle</span><span class="o">=</span><span class="mi">89</span><span class="p">):</span>
-</span><span id="L-503"><a href="#L-503"><span class="linenos">503</span></a>    <span class="sd">&quot;&quot;&quot;Third Angle of Triangle</span>
+</span><span id="L-503"><a href="#L-503"><span class="linenos">503</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Third Angle of Triangle</span>
 </span><span id="L-504"><a href="#L-504"><span class="linenos">504</span></a>
 </span><span id="L-505"><a href="#L-505"><span class="linenos">505</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-506"><a href="#L-506"><span class="linenos">506</span></a><span class="sd">    | --- | --- |</span>
@@ -692,7 +692,7 @@
 </span><span id="L-515"><a href="#L-515"><span class="linenos">515</span></a>
 </span><span id="L-516"><a href="#L-516"><span class="linenos">516</span></a>
 </span><span id="L-517"><a href="#L-517"><span class="linenos">517</span></a><span class="k">def</span> <span class="nf">valid_triangle</span><span class="p">(</span><span class="n">max_side_length</span><span class="o">=</span><span class="mi">50</span><span class="p">):</span>
-</span><span id="L-518"><a href="#L-518"><span class="linenos">518</span></a>    <span class="sd">&quot;&quot;&quot;Valid Triangle</span>
+</span><span id="L-518"><a href="#L-518"><span class="linenos">518</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Valid Triangle</span>
 </span><span id="L-519"><a href="#L-519"><span class="linenos">519</span></a>
 </span><span id="L-520"><a href="#L-520"><span class="linenos">520</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-521"><a href="#L-521"><span class="linenos">521</span></a><span class="sd">    | --- | --- |</span>
@@ -714,7 +714,7 @@
 </span><span id="L-537"><a href="#L-537"><span class="linenos">537</span></a>
 </span><span id="L-538"><a href="#L-538"><span class="linenos">538</span></a>
 </span><span id="L-539"><a href="#L-539"><span class="linenos">539</span></a><span class="k">def</span> <span class="nf">volume_cone</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_height</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="L-540"><a href="#L-540"><span class="linenos">540</span></a>    <span class="sd">&quot;&quot;&quot;Volume of a cone</span>
+</span><span id="L-540"><a href="#L-540"><span class="linenos">540</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Volume of a cone</span>
 </span><span id="L-541"><a href="#L-541"><span class="linenos">541</span></a>
 </span><span id="L-542"><a href="#L-542"><span class="linenos">542</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-543"><a href="#L-543"><span class="linenos">543</span></a><span class="sd">    | --- | --- |</span>
@@ -730,115 +730,116 @@
 </span><span id="L-553"><a href="#L-553"><span class="linenos">553</span></a>
 </span><span id="L-554"><a href="#L-554"><span class="linenos">554</span></a>
 </span><span id="L-555"><a href="#L-555"><span class="linenos">555</span></a><span class="k">def</span> <span class="nf">volume_cube</span><span class="p">(</span><span class="n">max_side</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="L-556"><a href="#L-556"><span class="linenos">556</span></a>    <span class="sd">&quot;&quot;&quot;Volume of a cube</span>
-</span><span id="L-557"><a href="#L-557"><span class="linenos">557</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
-</span><span id="L-558"><a href="#L-558"><span class="linenos">558</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="L-559"><a href="#L-559"><span class="linenos">559</span></a><span class="sd">    | Volume of a cube with a side length of $19m$ is | $6859 m^3$ |</span>
-</span><span id="L-560"><a href="#L-560"><span class="linenos">560</span></a><span class="sd">    &quot;&quot;&quot;</span>
-</span><span id="L-561"><a href="#L-561"><span class="linenos">561</span></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_side</span><span class="p">)</span>
-</span><span id="L-562"><a href="#L-562"><span class="linenos">562</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="n">a</span><span class="o">**</span><span class="mi">3</span>
-</span><span id="L-563"><a href="#L-563"><span class="linenos">563</span></a>
-</span><span id="L-564"><a href="#L-564"><span class="linenos">564</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of cube with a side length of $</span><span class="si">{</span><span class="n">a</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is&quot;</span>
-</span><span id="L-565"><a href="#L-565"><span class="linenos">565</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">^3$&quot;</span>
-</span><span id="L-566"><a href="#L-566"><span class="linenos">566</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
-</span><span id="L-567"><a href="#L-567"><span class="linenos">567</span></a>
+</span><span id="L-556"><a href="#L-556"><span class="linenos">556</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Volume of a cube</span>
+</span><span id="L-557"><a href="#L-557"><span class="linenos">557</span></a><span class="sd">    </span>
+</span><span id="L-558"><a href="#L-558"><span class="linenos">558</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
+</span><span id="L-559"><a href="#L-559"><span class="linenos">559</span></a><span class="sd">    | --- | --- |</span>
+</span><span id="L-560"><a href="#L-560"><span class="linenos">560</span></a><span class="sd">    | Volume of a cube with a side length of $19m$ is | $6859 m^3$ |</span>
+</span><span id="L-561"><a href="#L-561"><span class="linenos">561</span></a><span class="sd">    &quot;&quot;&quot;</span>
+</span><span id="L-562"><a href="#L-562"><span class="linenos">562</span></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_side</span><span class="p">)</span>
+</span><span id="L-563"><a href="#L-563"><span class="linenos">563</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="n">a</span><span class="o">**</span><span class="mi">3</span>
+</span><span id="L-564"><a href="#L-564"><span class="linenos">564</span></a>
+</span><span id="L-565"><a href="#L-565"><span class="linenos">565</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of cube with a side length of $</span><span class="si">{</span><span class="n">a</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is&quot;</span>
+</span><span id="L-566"><a href="#L-566"><span class="linenos">566</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">^3$&quot;</span>
+</span><span id="L-567"><a href="#L-567"><span class="linenos">567</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span><span id="L-568"><a href="#L-568"><span class="linenos">568</span></a>
-</span><span id="L-569"><a href="#L-569"><span class="linenos">569</span></a><span class="k">def</span> <span class="nf">volume_cuboid</span><span class="p">(</span><span class="n">max_side</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="L-570"><a href="#L-570"><span class="linenos">570</span></a>    <span class="sd">&quot;&quot;&quot;Volume of a cuboid</span>
-</span><span id="L-571"><a href="#L-571"><span class="linenos">571</span></a>
-</span><span id="L-572"><a href="#L-572"><span class="linenos">572</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
-</span><span id="L-573"><a href="#L-573"><span class="linenos">573</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="L-574"><a href="#L-574"><span class="linenos">574</span></a><span class="sd">    | Volume of cuboid with sides = $17m, 11m, 13m$ is | $2431 m^3$ |</span>
-</span><span id="L-575"><a href="#L-575"><span class="linenos">575</span></a><span class="sd">    &quot;&quot;&quot;</span>
-</span><span id="L-576"><a href="#L-576"><span class="linenos">576</span></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_side</span><span class="p">)</span>
-</span><span id="L-577"><a href="#L-577"><span class="linenos">577</span></a>    <span class="n">b</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_side</span><span class="p">)</span>
-</span><span id="L-578"><a href="#L-578"><span class="linenos">578</span></a>    <span class="n">c</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_side</span><span class="p">)</span>
-</span><span id="L-579"><a href="#L-579"><span class="linenos">579</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="n">a</span> <span class="o">*</span> <span class="n">b</span> <span class="o">*</span> <span class="n">c</span>
-</span><span id="L-580"><a href="#L-580"><span class="linenos">580</span></a>
-</span><span id="L-581"><a href="#L-581"><span class="linenos">581</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of cuboid with sides = $</span><span class="si">{</span><span class="n">a</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">, </span><span class="si">{</span><span class="n">b</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">, </span><span class="si">{</span><span class="n">c</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is&quot;</span>
-</span><span id="L-582"><a href="#L-582"><span class="linenos">582</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">^3$&quot;</span>
-</span><span id="L-583"><a href="#L-583"><span class="linenos">583</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
-</span><span id="L-584"><a href="#L-584"><span class="linenos">584</span></a>
+</span><span id="L-569"><a href="#L-569"><span class="linenos">569</span></a>
+</span><span id="L-570"><a href="#L-570"><span class="linenos">570</span></a><span class="k">def</span> <span class="nf">volume_cuboid</span><span class="p">(</span><span class="n">max_side</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
+</span><span id="L-571"><a href="#L-571"><span class="linenos">571</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Volume of a cuboid</span>
+</span><span id="L-572"><a href="#L-572"><span class="linenos">572</span></a>
+</span><span id="L-573"><a href="#L-573"><span class="linenos">573</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
+</span><span id="L-574"><a href="#L-574"><span class="linenos">574</span></a><span class="sd">    | --- | --- |</span>
+</span><span id="L-575"><a href="#L-575"><span class="linenos">575</span></a><span class="sd">    | Volume of cuboid with sides = $17m, 11m, 13m$ is | $2431 m^3$ |</span>
+</span><span id="L-576"><a href="#L-576"><span class="linenos">576</span></a><span class="sd">    &quot;&quot;&quot;</span>
+</span><span id="L-577"><a href="#L-577"><span class="linenos">577</span></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_side</span><span class="p">)</span>
+</span><span id="L-578"><a href="#L-578"><span class="linenos">578</span></a>    <span class="n">b</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_side</span><span class="p">)</span>
+</span><span id="L-579"><a href="#L-579"><span class="linenos">579</span></a>    <span class="n">c</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_side</span><span class="p">)</span>
+</span><span id="L-580"><a href="#L-580"><span class="linenos">580</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="n">a</span> <span class="o">*</span> <span class="n">b</span> <span class="o">*</span> <span class="n">c</span>
+</span><span id="L-581"><a href="#L-581"><span class="linenos">581</span></a>
+</span><span id="L-582"><a href="#L-582"><span class="linenos">582</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of cuboid with sides = $</span><span class="si">{</span><span class="n">a</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">, </span><span class="si">{</span><span class="n">b</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">, </span><span class="si">{</span><span class="n">c</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is&quot;</span>
+</span><span id="L-583"><a href="#L-583"><span class="linenos">583</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">^3$&quot;</span>
+</span><span id="L-584"><a href="#L-584"><span class="linenos">584</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span><span id="L-585"><a href="#L-585"><span class="linenos">585</span></a>
-</span><span id="L-586"><a href="#L-586"><span class="linenos">586</span></a><span class="k">def</span> <span class="nf">volume_cylinder</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_height</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="L-587"><a href="#L-587"><span class="linenos">587</span></a>    <span class="sd">&quot;&quot;&quot;Volume of a cylinder</span>
-</span><span id="L-588"><a href="#L-588"><span class="linenos">588</span></a>
-</span><span id="L-589"><a href="#L-589"><span class="linenos">589</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
-</span><span id="L-590"><a href="#L-590"><span class="linenos">590</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="L-591"><a href="#L-591"><span class="linenos">591</span></a><span class="sd">    | Volume of cylinder with height $= 3m$ and radius $= 10m$ is | $942 m^3$ |</span>
-</span><span id="L-592"><a href="#L-592"><span class="linenos">592</span></a><span class="sd">    &quot;&quot;&quot;</span>
-</span><span id="L-593"><a href="#L-593"><span class="linenos">593</span></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_height</span><span class="p">)</span>
-</span><span id="L-594"><a href="#L-594"><span class="linenos">594</span></a>    <span class="n">b</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_radius</span><span class="p">)</span>
-</span><span id="L-595"><a href="#L-595"><span class="linenos">595</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">b</span> <span class="o">*</span> <span class="n">b</span> <span class="o">*</span> <span class="n">a</span><span class="p">)</span>
-</span><span id="L-596"><a href="#L-596"><span class="linenos">596</span></a>
-</span><span id="L-597"><a href="#L-597"><span class="linenos">597</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of cylinder with height $= </span><span class="si">{</span><span class="n">a</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ and radius $= </span><span class="si">{</span><span class="n">b</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is&quot;</span>
-</span><span id="L-598"><a href="#L-598"><span class="linenos">598</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">^3$&quot;</span>
-</span><span id="L-599"><a href="#L-599"><span class="linenos">599</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
-</span><span id="L-600"><a href="#L-600"><span class="linenos">600</span></a>
+</span><span id="L-586"><a href="#L-586"><span class="linenos">586</span></a>
+</span><span id="L-587"><a href="#L-587"><span class="linenos">587</span></a><span class="k">def</span> <span class="nf">volume_cylinder</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_height</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
+</span><span id="L-588"><a href="#L-588"><span class="linenos">588</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Volume of a cylinder</span>
+</span><span id="L-589"><a href="#L-589"><span class="linenos">589</span></a>
+</span><span id="L-590"><a href="#L-590"><span class="linenos">590</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
+</span><span id="L-591"><a href="#L-591"><span class="linenos">591</span></a><span class="sd">    | --- | --- |</span>
+</span><span id="L-592"><a href="#L-592"><span class="linenos">592</span></a><span class="sd">    | Volume of cylinder with height $= 3m$ and radius $= 10m$ is | $942 m^3$ |</span>
+</span><span id="L-593"><a href="#L-593"><span class="linenos">593</span></a><span class="sd">    &quot;&quot;&quot;</span>
+</span><span id="L-594"><a href="#L-594"><span class="linenos">594</span></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_height</span><span class="p">)</span>
+</span><span id="L-595"><a href="#L-595"><span class="linenos">595</span></a>    <span class="n">b</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_radius</span><span class="p">)</span>
+</span><span id="L-596"><a href="#L-596"><span class="linenos">596</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">b</span> <span class="o">*</span> <span class="n">b</span> <span class="o">*</span> <span class="n">a</span><span class="p">)</span>
+</span><span id="L-597"><a href="#L-597"><span class="linenos">597</span></a>
+</span><span id="L-598"><a href="#L-598"><span class="linenos">598</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of cylinder with height $= </span><span class="si">{</span><span class="n">a</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ and radius $= </span><span class="si">{</span><span class="n">b</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is&quot;</span>
+</span><span id="L-599"><a href="#L-599"><span class="linenos">599</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">^3$&quot;</span>
+</span><span id="L-600"><a href="#L-600"><span class="linenos">600</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span><span id="L-601"><a href="#L-601"><span class="linenos">601</span></a>
-</span><span id="L-602"><a href="#L-602"><span class="linenos">602</span></a><span class="k">def</span> <span class="nf">volume_cone_frustum</span><span class="p">(</span><span class="n">max_r1</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_r2</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_height</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="L-603"><a href="#L-603"><span class="linenos">603</span></a>    <span class="sd">&quot;&quot;&quot;Volume of the frustum of a cone</span>
-</span><span id="L-604"><a href="#L-604"><span class="linenos">604</span></a>
-</span><span id="L-605"><a href="#L-605"><span class="linenos">605</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
-</span><span id="L-606"><a href="#L-606"><span class="linenos">606</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="L-607"><a href="#L-607"><span class="linenos">607</span></a><span class="sd">    | Volume of frustum with height $= 30m$ and $r1 = 20m$ is and $r2 = 8m$ is | $19603.54 m^3$ |</span>
-</span><span id="L-608"><a href="#L-608"><span class="linenos">608</span></a><span class="sd">    &quot;&quot;&quot;</span>
-</span><span id="L-609"><a href="#L-609"><span class="linenos">609</span></a>    <span class="n">h</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_height</span><span class="p">)</span>
-</span><span id="L-610"><a href="#L-610"><span class="linenos">610</span></a>    <span class="n">r1</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_r1</span><span class="p">)</span>
-</span><span id="L-611"><a href="#L-611"><span class="linenos">611</span></a>    <span class="n">r2</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_r2</span><span class="p">)</span>
-</span><span id="L-612"><a href="#L-612"><span class="linenos">612</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(((</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">h</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">r1</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">r2</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">r1</span> <span class="o">*</span> <span class="n">r2</span><span class="p">))</span> <span class="o">/</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-</span><span id="L-613"><a href="#L-613"><span class="linenos">613</span></a>
-</span><span id="L-614"><a href="#L-614"><span class="linenos">614</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of frustum with height $= </span><span class="si">{</span><span class="n">h</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ and $r1 = </span><span class="si">{</span><span class="n">r1</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is and $r2 = </span><span class="si">{</span><span class="n">r2</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is &quot;</span>
-</span><span id="L-615"><a href="#L-615"><span class="linenos">615</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">^3$&quot;</span>
-</span><span id="L-616"><a href="#L-616"><span class="linenos">616</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
-</span><span id="L-617"><a href="#L-617"><span class="linenos">617</span></a>
+</span><span id="L-602"><a href="#L-602"><span class="linenos">602</span></a>
+</span><span id="L-603"><a href="#L-603"><span class="linenos">603</span></a><span class="k">def</span> <span class="nf">volume_cone_frustum</span><span class="p">(</span><span class="n">max_r1</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_r2</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_height</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
+</span><span id="L-604"><a href="#L-604"><span class="linenos">604</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Volume of the frustum of a cone</span>
+</span><span id="L-605"><a href="#L-605"><span class="linenos">605</span></a>
+</span><span id="L-606"><a href="#L-606"><span class="linenos">606</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
+</span><span id="L-607"><a href="#L-607"><span class="linenos">607</span></a><span class="sd">    | --- | --- |</span>
+</span><span id="L-608"><a href="#L-608"><span class="linenos">608</span></a><span class="sd">    | Volume of frustum with height $= 30m$ and $r1 = 20m$ is and $r2 = 8m$ is | $19603.54 m^3$ |</span>
+</span><span id="L-609"><a href="#L-609"><span class="linenos">609</span></a><span class="sd">    &quot;&quot;&quot;</span>
+</span><span id="L-610"><a href="#L-610"><span class="linenos">610</span></a>    <span class="n">h</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_height</span><span class="p">)</span>
+</span><span id="L-611"><a href="#L-611"><span class="linenos">611</span></a>    <span class="n">r1</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_r1</span><span class="p">)</span>
+</span><span id="L-612"><a href="#L-612"><span class="linenos">612</span></a>    <span class="n">r2</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_r2</span><span class="p">)</span>
+</span><span id="L-613"><a href="#L-613"><span class="linenos">613</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(((</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">h</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">r1</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">r2</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">r1</span> <span class="o">*</span> <span class="n">r2</span><span class="p">))</span> <span class="o">/</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
+</span><span id="L-614"><a href="#L-614"><span class="linenos">614</span></a>
+</span><span id="L-615"><a href="#L-615"><span class="linenos">615</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of frustum with height $= </span><span class="si">{</span><span class="n">h</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ and $r1 = </span><span class="si">{</span><span class="n">r1</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is and $r2 = </span><span class="si">{</span><span class="n">r2</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is &quot;</span>
+</span><span id="L-616"><a href="#L-616"><span class="linenos">616</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">^3$&quot;</span>
+</span><span id="L-617"><a href="#L-617"><span class="linenos">617</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span><span id="L-618"><a href="#L-618"><span class="linenos">618</span></a>
-</span><span id="L-619"><a href="#L-619"><span class="linenos">619</span></a><span class="k">def</span> <span class="nf">volume_hemisphere</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="L-620"><a href="#L-620"><span class="linenos">620</span></a>    <span class="sd">&quot;&quot;&quot;Volume of a hemisphere</span>
-</span><span id="L-621"><a href="#L-621"><span class="linenos">621</span></a>
-</span><span id="L-622"><a href="#L-622"><span class="linenos">622</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
-</span><span id="L-623"><a href="#L-623"><span class="linenos">623</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="L-624"><a href="#L-624"><span class="linenos">624</span></a><span class="sd">    | Volume of hemisphere with radius $32m =$ | $68629.14 m^3$ |</span>
-</span><span id="L-625"><a href="#L-625"><span class="linenos">625</span></a><span class="sd">    &quot;&quot;&quot;</span>
-</span><span id="L-626"><a href="#L-626"><span class="linenos">626</span></a>    <span class="n">r</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_radius</span><span class="p">)</span>
-</span><span id="L-627"><a href="#L-627"><span class="linenos">627</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="mi">2</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span> <span class="o">/</span> <span class="mi">3</span><span class="p">)</span> <span class="o">*</span> <span class="n">r</span><span class="o">**</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-</span><span id="L-628"><a href="#L-628"><span class="linenos">628</span></a>
-</span><span id="L-629"><a href="#L-629"><span class="linenos">629</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of hemisphere with radius $</span><span class="si">{</span><span class="n">r</span><span class="si">}</span><span class="s2"> m =$ &quot;</span>
-</span><span id="L-630"><a href="#L-630"><span class="linenos">630</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> m^3$&quot;</span>
-</span><span id="L-631"><a href="#L-631"><span class="linenos">631</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
-</span><span id="L-632"><a href="#L-632"><span class="linenos">632</span></a>
+</span><span id="L-619"><a href="#L-619"><span class="linenos">619</span></a>
+</span><span id="L-620"><a href="#L-620"><span class="linenos">620</span></a><span class="k">def</span> <span class="nf">volume_hemisphere</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
+</span><span id="L-621"><a href="#L-621"><span class="linenos">621</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Volume of a hemisphere</span>
+</span><span id="L-622"><a href="#L-622"><span class="linenos">622</span></a>
+</span><span id="L-623"><a href="#L-623"><span class="linenos">623</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
+</span><span id="L-624"><a href="#L-624"><span class="linenos">624</span></a><span class="sd">    | --- | --- |</span>
+</span><span id="L-625"><a href="#L-625"><span class="linenos">625</span></a><span class="sd">    | Volume of hemisphere with radius $32m =$ | $68629.14 m^3$ |</span>
+</span><span id="L-626"><a href="#L-626"><span class="linenos">626</span></a><span class="sd">    &quot;&quot;&quot;</span>
+</span><span id="L-627"><a href="#L-627"><span class="linenos">627</span></a>    <span class="n">r</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_radius</span><span class="p">)</span>
+</span><span id="L-628"><a href="#L-628"><span class="linenos">628</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="mi">2</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span> <span class="o">/</span> <span class="mi">3</span><span class="p">)</span> <span class="o">*</span> <span class="n">r</span><span class="o">**</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
+</span><span id="L-629"><a href="#L-629"><span class="linenos">629</span></a>
+</span><span id="L-630"><a href="#L-630"><span class="linenos">630</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of hemisphere with radius $</span><span class="si">{</span><span class="n">r</span><span class="si">}</span><span class="s2"> m =$ &quot;</span>
+</span><span id="L-631"><a href="#L-631"><span class="linenos">631</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> m^3$&quot;</span>
+</span><span id="L-632"><a href="#L-632"><span class="linenos">632</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span><span id="L-633"><a href="#L-633"><span class="linenos">633</span></a>
-</span><span id="L-634"><a href="#L-634"><span class="linenos">634</span></a><span class="k">def</span> <span class="nf">volume_pyramid</span><span class="p">(</span><span class="n">max_length</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_width</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_height</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="L-635"><a href="#L-635"><span class="linenos">635</span></a>    <span class="sd">&quot;&quot;&quot;Volume of a pyramid</span>
-</span><span id="L-636"><a href="#L-636"><span class="linenos">636</span></a>
-</span><span id="L-637"><a href="#L-637"><span class="linenos">637</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
-</span><span id="L-638"><a href="#L-638"><span class="linenos">638</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="L-639"><a href="#L-639"><span class="linenos">639</span></a><span class="sd">    | Volume of pyramid with base length $= 7 m$, base width $= 18 m$ and height $= 42 m$ is | $1764.0 m^3$ |</span>
-</span><span id="L-640"><a href="#L-640"><span class="linenos">640</span></a><span class="sd">    &quot;&quot;&quot;</span>
-</span><span id="L-641"><a href="#L-641"><span class="linenos">641</span></a>    <span class="n">length</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_length</span><span class="p">)</span>
-</span><span id="L-642"><a href="#L-642"><span class="linenos">642</span></a>    <span class="n">width</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_width</span><span class="p">)</span>
-</span><span id="L-643"><a href="#L-643"><span class="linenos">643</span></a>    <span class="n">height</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_height</span><span class="p">)</span>
-</span><span id="L-644"><a href="#L-644"><span class="linenos">644</span></a>
-</span><span id="L-645"><a href="#L-645"><span class="linenos">645</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="n">length</span> <span class="o">*</span> <span class="n">width</span> <span class="o">*</span> <span class="n">height</span><span class="p">)</span> <span class="o">/</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-</span><span id="L-646"><a href="#L-646"><span class="linenos">646</span></a>
-</span><span id="L-647"><a href="#L-647"><span class="linenos">647</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of pyramid with base length $= </span><span class="si">{</span><span class="n">length</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$, base width $= </span><span class="si">{</span><span class="n">width</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ and height $= </span><span class="si">{</span><span class="n">height</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is&quot;</span>
-</span><span id="L-648"><a href="#L-648"><span class="linenos">648</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">^3$&quot;</span>
-</span><span id="L-649"><a href="#L-649"><span class="linenos">649</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
-</span><span id="L-650"><a href="#L-650"><span class="linenos">650</span></a>
+</span><span id="L-634"><a href="#L-634"><span class="linenos">634</span></a>
+</span><span id="L-635"><a href="#L-635"><span class="linenos">635</span></a><span class="k">def</span> <span class="nf">volume_pyramid</span><span class="p">(</span><span class="n">max_length</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_width</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_height</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
+</span><span id="L-636"><a href="#L-636"><span class="linenos">636</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Volume of a pyramid</span>
+</span><span id="L-637"><a href="#L-637"><span class="linenos">637</span></a>
+</span><span id="L-638"><a href="#L-638"><span class="linenos">638</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
+</span><span id="L-639"><a href="#L-639"><span class="linenos">639</span></a><span class="sd">    | --- | --- |</span>
+</span><span id="L-640"><a href="#L-640"><span class="linenos">640</span></a><span class="sd">    | Volume of pyramid with base length $= 7 m$, base width $= 18 m$ and height $= 42 m$ is | $1764.0 m^3$ |</span>
+</span><span id="L-641"><a href="#L-641"><span class="linenos">641</span></a><span class="sd">    &quot;&quot;&quot;</span>
+</span><span id="L-642"><a href="#L-642"><span class="linenos">642</span></a>    <span class="n">length</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_length</span><span class="p">)</span>
+</span><span id="L-643"><a href="#L-643"><span class="linenos">643</span></a>    <span class="n">width</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_width</span><span class="p">)</span>
+</span><span id="L-644"><a href="#L-644"><span class="linenos">644</span></a>    <span class="n">height</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_height</span><span class="p">)</span>
+</span><span id="L-645"><a href="#L-645"><span class="linenos">645</span></a>
+</span><span id="L-646"><a href="#L-646"><span class="linenos">646</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="n">length</span> <span class="o">*</span> <span class="n">width</span> <span class="o">*</span> <span class="n">height</span><span class="p">)</span> <span class="o">/</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
+</span><span id="L-647"><a href="#L-647"><span class="linenos">647</span></a>
+</span><span id="L-648"><a href="#L-648"><span class="linenos">648</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of pyramid with base length $= </span><span class="si">{</span><span class="n">length</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$, base width $= </span><span class="si">{</span><span class="n">width</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ and height $= </span><span class="si">{</span><span class="n">height</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is&quot;</span>
+</span><span id="L-649"><a href="#L-649"><span class="linenos">649</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">^3$&quot;</span>
+</span><span id="L-650"><a href="#L-650"><span class="linenos">650</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span><span id="L-651"><a href="#L-651"><span class="linenos">651</span></a>
-</span><span id="L-652"><a href="#L-652"><span class="linenos">652</span></a><span class="k">def</span> <span class="nf">volume_sphere</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="L-653"><a href="#L-653"><span class="linenos">653</span></a>    <span class="sd">&quot;&quot;&quot;Volume of a sphere</span>
-</span><span id="L-654"><a href="#L-654"><span class="linenos">654</span></a>
-</span><span id="L-655"><a href="#L-655"><span class="linenos">655</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
-</span><span id="L-656"><a href="#L-656"><span class="linenos">656</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="L-657"><a href="#L-657"><span class="linenos">657</span></a><span class="sd">    | Volume of sphere with radius $30 m = $ | $113097.36 m^3$ |</span>
-</span><span id="L-658"><a href="#L-658"><span class="linenos">658</span></a><span class="sd">    &quot;&quot;&quot;</span>
-</span><span id="L-659"><a href="#L-659"><span class="linenos">659</span></a>    <span class="n">r</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_radius</span><span class="p">)</span>
-</span><span id="L-660"><a href="#L-660"><span class="linenos">660</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="mi">4</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span> <span class="o">/</span> <span class="mi">3</span><span class="p">)</span> <span class="o">*</span> <span class="n">r</span><span class="o">**</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-</span><span id="L-661"><a href="#L-661"><span class="linenos">661</span></a>
-</span><span id="L-662"><a href="#L-662"><span class="linenos">662</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of sphere with radius $</span><span class="si">{</span><span class="n">r</span><span class="si">}</span><span class="s2"> m = $&quot;</span>
-</span><span id="L-663"><a href="#L-663"><span class="linenos">663</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> m^3$&quot;</span>
-</span><span id="L-664"><a href="#L-664"><span class="linenos">664</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
+</span><span id="L-652"><a href="#L-652"><span class="linenos">652</span></a>
+</span><span id="L-653"><a href="#L-653"><span class="linenos">653</span></a><span class="k">def</span> <span class="nf">volume_sphere</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
+</span><span id="L-654"><a href="#L-654"><span class="linenos">654</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Volume of a sphere</span>
+</span><span id="L-655"><a href="#L-655"><span class="linenos">655</span></a>
+</span><span id="L-656"><a href="#L-656"><span class="linenos">656</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
+</span><span id="L-657"><a href="#L-657"><span class="linenos">657</span></a><span class="sd">    | --- | --- |</span>
+</span><span id="L-658"><a href="#L-658"><span class="linenos">658</span></a><span class="sd">    | Volume of sphere with radius $30 m = $ | $113097.36 m^3$ |</span>
+</span><span id="L-659"><a href="#L-659"><span class="linenos">659</span></a><span class="sd">    &quot;&quot;&quot;</span>
+</span><span id="L-660"><a href="#L-660"><span class="linenos">660</span></a>    <span class="n">r</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_radius</span><span class="p">)</span>
+</span><span id="L-661"><a href="#L-661"><span class="linenos">661</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="mi">4</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span> <span class="o">/</span> <span class="mi">3</span><span class="p">)</span> <span class="o">*</span> <span class="n">r</span><span class="o">**</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
+</span><span id="L-662"><a href="#L-662"><span class="linenos">662</span></a>
+</span><span id="L-663"><a href="#L-663"><span class="linenos">663</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of sphere with radius $</span><span class="si">{</span><span class="n">r</span><span class="si">}</span><span class="s2"> m = $&quot;</span>
+</span><span id="L-664"><a href="#L-664"><span class="linenos">664</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> m^3$&quot;</span>
+</span><span id="L-665"><a href="#L-665"><span class="linenos">665</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span></pre></div>
 
 
@@ -855,7 +856,7 @@
     </div>
     <a class="headerlink" href="#angle_btw_vectors"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="angle_btw_vectors-7"><a href="#angle_btw_vectors-7"><span class="linenos"> 7</span></a><span class="k">def</span> <span class="nf">angle_btw_vectors</span><span class="p">(</span><span class="n">max_elt_amt</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="angle_btw_vectors-8"><a href="#angle_btw_vectors-8"><span class="linenos"> 8</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Angle between 2 vectors</span>
+</span><span id="angle_btw_vectors-8"><a href="#angle_btw_vectors-8"><span class="linenos"> 8</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Angle between 2 vectors</span>
 </span><span id="angle_btw_vectors-9"><a href="#angle_btw_vectors-9"><span class="linenos"> 9</span></a>
 </span><span id="angle_btw_vectors-10"><a href="#angle_btw_vectors-10"><span class="linenos">10</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="angle_btw_vectors-11"><a href="#angle_btw_vectors-11"><span class="linenos">11</span></a><span class="sd">    | --- | --- |</span>
@@ -919,7 +920,7 @@
     </div>
     <a class="headerlink" href="#angle_regular_polygon"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="angle_regular_polygon-39"><a href="#angle_regular_polygon-39"><span class="linenos">39</span></a><span class="k">def</span> <span class="nf">angle_regular_polygon</span><span class="p">(</span><span class="n">min_val</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">max_val</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="angle_regular_polygon-40"><a href="#angle_regular_polygon-40"><span class="linenos">40</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Angle of a Regular Polygon</span>
+</span><span id="angle_regular_polygon-40"><a href="#angle_regular_polygon-40"><span class="linenos">40</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Angle of a Regular Polygon</span>
 </span><span id="angle_regular_polygon-41"><a href="#angle_regular_polygon-41"><span class="linenos">41</span></a>
 </span><span id="angle_regular_polygon-42"><a href="#angle_regular_polygon-42"><span class="linenos">42</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="angle_regular_polygon-43"><a href="#angle_regular_polygon-43"><span class="linenos">43</span></a><span class="sd">    | --- | --- |</span>
@@ -929,7 +930,7 @@
 </span><span id="angle_regular_polygon-47"><a href="#angle_regular_polygon-47"><span class="linenos">47</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Find the angle of a regular polygon with $</span><span class="si">{</span><span class="n">sideNum</span><span class="si">}</span><span class="s2">$ sides&quot;</span>
 </span><span id="angle_regular_polygon-48"><a href="#angle_regular_polygon-48"><span class="linenos">48</span></a>
 </span><span id="angle_regular_polygon-49"><a href="#angle_regular_polygon-49"><span class="linenos">49</span></a>    <span class="n">exteriorAngle</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="mi">360</span> <span class="o">/</span> <span class="n">sideNum</span><span class="p">),</span> <span class="mi">2</span><span class="p">)</span>
-</span><span id="angle_regular_polygon-50"><a href="#angle_regular_polygon-50"><span class="linenos">50</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="mi">180</span> <span class="o">-</span> <span class="n">exteriorAngle</span><span class="si">}</span><span class="s1">$&#39;</span>
+</span><span id="angle_regular_polygon-50"><a href="#angle_regular_polygon-50"><span class="linenos">50</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="mi">180</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">exteriorAngle</span><span class="si">}</span><span class="s1">$&#39;</span>
 </span><span id="angle_regular_polygon-51"><a href="#angle_regular_polygon-51"><span class="linenos">51</span></a>
 </span><span id="angle_regular_polygon-52"><a href="#angle_regular_polygon-52"><span class="linenos">52</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span></pre></div>
@@ -967,7 +968,7 @@
     </div>
     <a class="headerlink" href="#arc_length"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="arc_length-55"><a href="#arc_length-55"><span class="linenos">55</span></a><span class="k">def</span> <span class="nf">arc_length</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">49</span><span class="p">,</span> <span class="n">max_angle</span><span class="o">=</span><span class="mi">359</span><span class="p">):</span>
-</span><span id="arc_length-56"><a href="#arc_length-56"><span class="linenos">56</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Arc length of Angle</span>
+</span><span id="arc_length-56"><a href="#arc_length-56"><span class="linenos">56</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Arc length of Angle</span>
 </span><span id="arc_length-57"><a href="#arc_length-57"><span class="linenos">57</span></a>
 </span><span id="arc_length-58"><a href="#arc_length-58"><span class="linenos">58</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="arc_length-59"><a href="#arc_length-59"><span class="linenos">59</span></a><span class="sd">    | --- | --- |</span>
@@ -1016,7 +1017,7 @@
     </div>
     <a class="headerlink" href="#area_of_circle"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="area_of_circle-72"><a href="#area_of_circle-72"><span class="linenos">72</span></a><span class="k">def</span> <span class="nf">area_of_circle</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="area_of_circle-73"><a href="#area_of_circle-73"><span class="linenos">73</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Area of Circle</span>
+</span><span id="area_of_circle-73"><a href="#area_of_circle-73"><span class="linenos">73</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Area of Circle</span>
 </span><span id="area_of_circle-74"><a href="#area_of_circle-74"><span class="linenos">74</span></a>
 </span><span id="area_of_circle-75"><a href="#area_of_circle-75"><span class="linenos">75</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="area_of_circle-76"><a href="#area_of_circle-76"><span class="linenos">76</span></a><span class="sd">    | --- | --- |</span>
@@ -1062,7 +1063,7 @@
     </div>
     <a class="headerlink" href="#area_of_circle_given_center_and_point"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="area_of_circle_given_center_and_point-86"><a href="#area_of_circle_given_center_and_point-86"><span class="linenos"> 86</span></a><span class="k">def</span> <span class="nf">area_of_circle_given_center_and_point</span><span class="p">(</span><span class="n">max_coordinate</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">max_radius</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="area_of_circle_given_center_and_point-87"><a href="#area_of_circle_given_center_and_point-87"><span class="linenos"> 87</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Area of Circle given center and a point on circle</span>
+</span><span id="area_of_circle_given_center_and_point-87"><a href="#area_of_circle_given_center_and_point-87"><span class="linenos"> 87</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Area of Circle given center and a point on circle</span>
 </span><span id="area_of_circle_given_center_and_point-88"><a href="#area_of_circle_given_center_and_point-88"><span class="linenos"> 88</span></a>
 </span><span id="area_of_circle_given_center_and_point-89"><a href="#area_of_circle_given_center_and_point-89"><span class="linenos"> 89</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="area_of_circle_given_center_and_point-90"><a href="#area_of_circle_given_center_and_point-90"><span class="linenos"> 90</span></a><span class="sd">    | --- | --- |</span>
@@ -1116,7 +1117,7 @@
     </div>
     <a class="headerlink" href="#area_of_triangle"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="area_of_triangle-108"><a href="#area_of_triangle-108"><span class="linenos">108</span></a><span class="k">def</span> <span class="nf">area_of_triangle</span><span class="p">(</span><span class="n">max_a</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_b</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="area_of_triangle-109"><a href="#area_of_triangle-109"><span class="linenos">109</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Area of Triangle</span>
+</span><span id="area_of_triangle-109"><a href="#area_of_triangle-109"><span class="linenos">109</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Area of Triangle</span>
 </span><span id="area_of_triangle-110"><a href="#area_of_triangle-110"><span class="linenos">110</span></a>
 </span><span id="area_of_triangle-111"><a href="#area_of_triangle-111"><span class="linenos">111</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="area_of_triangle-112"><a href="#area_of_triangle-112"><span class="linenos">112</span></a><span class="sd">    | --- | --- |</span>
@@ -1130,7 +1131,7 @@
 </span><span id="area_of_triangle-120"><a href="#area_of_triangle-120"><span class="linenos">120</span></a>    <span class="n">area</span> <span class="o">=</span> <span class="p">(</span><span class="n">s</span> <span class="o">*</span> <span class="p">(</span><span class="n">s</span> <span class="o">-</span> <span class="n">a</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">s</span> <span class="o">-</span> <span class="n">b</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">s</span> <span class="o">-</span> <span class="n">c</span><span class="p">))</span><span class="o">**</span><span class="mf">0.5</span>
 </span><span id="area_of_triangle-121"><a href="#area_of_triangle-121"><span class="linenos">121</span></a>
 </span><span id="area_of_triangle-122"><a href="#area_of_triangle-122"><span class="linenos">122</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Area of triangle with side lengths: $</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="s2">, </span><span class="si">{</span><span class="n">b</span><span class="si">}</span><span class="s2">, </span><span class="si">{</span><span class="n">c</span><span class="si">}</span><span class="s2"> = $&quot;</span>
-</span><span id="area_of_triangle-123"><a href="#area_of_triangle-123"><span class="linenos">123</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="nb">round</span><span class="p">(</span><span class="n">area</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span><span class="si">}</span><span class="s1">$&#39;</span>
+</span><span id="area_of_triangle-123"><a href="#area_of_triangle-123"><span class="linenos">123</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="nb">round</span><span class="p">(</span><span class="n">area</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="si">}</span><span class="s1">$&#39;</span>
 </span><span id="area_of_triangle-124"><a href="#area_of_triangle-124"><span class="linenos">124</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span></pre></div>
 
@@ -1168,7 +1169,7 @@
     <a class="headerlink" href="#basic_trigonometry"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="basic_trigonometry-128"><a href="#basic_trigonometry-128"><span class="linenos">128</span></a><span class="k">def</span> <span class="nf">basic_trigonometry</span><span class="p">(</span><span class="n">angles</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">30</span><span class="p">,</span> <span class="mi">45</span><span class="p">,</span> <span class="mi">60</span><span class="p">,</span> <span class="mi">90</span><span class="p">],</span>
 </span><span id="basic_trigonometry-129"><a href="#basic_trigonometry-129"><span class="linenos">129</span></a>                       <span class="n">functions</span><span class="o">=</span><span class="p">[</span><span class="s2">&quot;sin&quot;</span><span class="p">,</span> <span class="s2">&quot;cos&quot;</span><span class="p">,</span> <span class="s2">&quot;tan&quot;</span><span class="p">]):</span>
-</span><span id="basic_trigonometry-130"><a href="#basic_trigonometry-130"><span class="linenos">130</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Trigonometric Values</span>
+</span><span id="basic_trigonometry-130"><a href="#basic_trigonometry-130"><span class="linenos">130</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Trigonometric Values</span>
 </span><span id="basic_trigonometry-131"><a href="#basic_trigonometry-131"><span class="linenos">131</span></a>
 </span><span id="basic_trigonometry-132"><a href="#basic_trigonometry-132"><span class="linenos">132</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="basic_trigonometry-133"><a href="#basic_trigonometry-133"><span class="linenos">133</span></a><span class="sd">    | --- | --- |</span>
@@ -1229,7 +1230,7 @@
     </div>
     <a class="headerlink" href="#circumference"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="circumference-158"><a href="#circumference-158"><span class="linenos">158</span></a><span class="k">def</span> <span class="nf">circumference</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="circumference-159"><a href="#circumference-159"><span class="linenos">159</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Circumference of Circle</span>
+</span><span id="circumference-159"><a href="#circumference-159"><span class="linenos">159</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Circumference of Circle</span>
 </span><span id="circumference-160"><a href="#circumference-160"><span class="linenos">160</span></a>
 </span><span id="circumference-161"><a href="#circumference-161"><span class="linenos">161</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="circumference-162"><a href="#circumference-162"><span class="linenos">162</span></a><span class="sd">    | --- | --- |</span>
@@ -1275,7 +1276,7 @@
     </div>
     <a class="headerlink" href="#complementary_and_supplementary_angle"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="complementary_and_supplementary_angle-172"><a href="#complementary_and_supplementary_angle-172"><span class="linenos">172</span></a><span class="k">def</span> <span class="nf">complementary_and_supplementary_angle</span><span class="p">(</span><span class="n">max_supp</span><span class="o">=</span><span class="mi">180</span><span class="p">,</span> <span class="n">max_comp</span><span class="o">=</span><span class="mi">90</span><span class="p">):</span>
-</span><span id="complementary_and_supplementary_angle-173"><a href="#complementary_and_supplementary_angle-173"><span class="linenos">173</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Complementary and Supplementary Angle</span>
+</span><span id="complementary_and_supplementary_angle-173"><a href="#complementary_and_supplementary_angle-173"><span class="linenos">173</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Complementary and Supplementary Angle</span>
 </span><span id="complementary_and_supplementary_angle-174"><a href="#complementary_and_supplementary_angle-174"><span class="linenos">174</span></a>
 </span><span id="complementary_and_supplementary_angle-175"><a href="#complementary_and_supplementary_angle-175"><span class="linenos">175</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="complementary_and_supplementary_angle-176"><a href="#complementary_and_supplementary_angle-176"><span class="linenos">176</span></a><span class="sd">    | --- | --- |</span>
@@ -1328,7 +1329,7 @@
     </div>
     <a class="headerlink" href="#curved_surface_area_cylinder"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="curved_surface_area_cylinder-193"><a href="#curved_surface_area_cylinder-193"><span class="linenos">193</span></a><span class="k">def</span> <span class="nf">curved_surface_area_cylinder</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">49</span><span class="p">,</span> <span class="n">max_height</span><span class="o">=</span><span class="mi">99</span><span class="p">):</span>
-</span><span id="curved_surface_area_cylinder-194"><a href="#curved_surface_area_cylinder-194"><span class="linenos">194</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Curved surface area of a cylinder</span>
+</span><span id="curved_surface_area_cylinder-194"><a href="#curved_surface_area_cylinder-194"><span class="linenos">194</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Curved surface area of a cylinder</span>
 </span><span id="curved_surface_area_cylinder-195"><a href="#curved_surface_area_cylinder-195"><span class="linenos">195</span></a>
 </span><span id="curved_surface_area_cylinder-196"><a href="#curved_surface_area_cylinder-196"><span class="linenos">196</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="curved_surface_area_cylinder-197"><a href="#curved_surface_area_cylinder-197"><span class="linenos">197</span></a><span class="sd">    | --- | --- |</span>
@@ -1377,7 +1378,7 @@
     </div>
     <a class="headerlink" href="#degree_to_rad"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="degree_to_rad-210"><a href="#degree_to_rad-210"><span class="linenos">210</span></a><span class="k">def</span> <span class="nf">degree_to_rad</span><span class="p">(</span><span class="n">max_deg</span><span class="o">=</span><span class="mi">360</span><span class="p">):</span>
-</span><span id="degree_to_rad-211"><a href="#degree_to_rad-211"><span class="linenos">211</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Degrees to Radians</span>
+</span><span id="degree_to_rad-211"><a href="#degree_to_rad-211"><span class="linenos">211</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Degrees to Radians</span>
 </span><span id="degree_to_rad-212"><a href="#degree_to_rad-212"><span class="linenos">212</span></a>
 </span><span id="degree_to_rad-213"><a href="#degree_to_rad-213"><span class="linenos">213</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="degree_to_rad-214"><a href="#degree_to_rad-214"><span class="linenos">214</span></a><span class="sd">    | --- | --- |</span>
@@ -1425,7 +1426,7 @@
     </div>
     <a class="headerlink" href="#equation_of_line_from_two_points"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="equation_of_line_from_two_points-226"><a href="#equation_of_line_from_two_points-226"><span class="linenos">226</span></a><span class="k">def</span> <span class="nf">equation_of_line_from_two_points</span><span class="p">(</span><span class="n">max_coordinate</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">min_coordinate</span><span class="o">=-</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="equation_of_line_from_two_points-227"><a href="#equation_of_line_from_two_points-227"><span class="linenos">227</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Equation of line from two points</span>
+</span><span id="equation_of_line_from_two_points-227"><a href="#equation_of_line_from_two_points-227"><span class="linenos">227</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Equation of line from two points</span>
 </span><span id="equation_of_line_from_two_points-228"><a href="#equation_of_line_from_two_points-228"><span class="linenos">228</span></a>
 </span><span id="equation_of_line_from_two_points-229"><a href="#equation_of_line_from_two_points-229"><span class="linenos">229</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="equation_of_line_from_two_points-230"><a href="#equation_of_line_from_two_points-230"><span class="linenos">230</span></a><span class="sd">    | --- | --- |</span>
@@ -1519,7 +1520,7 @@
     </div>
     <a class="headerlink" href="#fourth_angle_of_quadrilateral"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="fourth_angle_of_quadrilateral-288"><a href="#fourth_angle_of_quadrilateral-288"><span class="linenos">288</span></a><span class="k">def</span> <span class="nf">fourth_angle_of_quadrilateral</span><span class="p">(</span><span class="n">max_angle</span><span class="o">=</span><span class="mi">180</span><span class="p">):</span>
-</span><span id="fourth_angle_of_quadrilateral-289"><a href="#fourth_angle_of_quadrilateral-289"><span class="linenos">289</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Fourth Angle of Quadrilateral</span>
+</span><span id="fourth_angle_of_quadrilateral-289"><a href="#fourth_angle_of_quadrilateral-289"><span class="linenos">289</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Fourth Angle of Quadrilateral</span>
 </span><span id="fourth_angle_of_quadrilateral-290"><a href="#fourth_angle_of_quadrilateral-290"><span class="linenos">290</span></a>
 </span><span id="fourth_angle_of_quadrilateral-291"><a href="#fourth_angle_of_quadrilateral-291"><span class="linenos">291</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="fourth_angle_of_quadrilateral-292"><a href="#fourth_angle_of_quadrilateral-292"><span class="linenos">292</span></a><span class="sd">    | --- | --- |</span>
@@ -1570,7 +1571,7 @@
     </div>
     <a class="headerlink" href="#perimeter_of_polygons"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="perimeter_of_polygons-307"><a href="#perimeter_of_polygons-307"><span class="linenos">307</span></a><span class="k">def</span> <span class="nf">perimeter_of_polygons</span><span class="p">(</span><span class="n">max_sides</span><span class="o">=</span><span class="mi">12</span><span class="p">,</span> <span class="n">max_length</span><span class="o">=</span><span class="mi">120</span><span class="p">):</span>
-</span><span id="perimeter_of_polygons-308"><a href="#perimeter_of_polygons-308"><span class="linenos">308</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Perimeter of Polygons</span>
+</span><span id="perimeter_of_polygons-308"><a href="#perimeter_of_polygons-308"><span class="linenos">308</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Perimeter of Polygons</span>
 </span><span id="perimeter_of_polygons-309"><a href="#perimeter_of_polygons-309"><span class="linenos">309</span></a>
 </span><span id="perimeter_of_polygons-310"><a href="#perimeter_of_polygons-310"><span class="linenos">310</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="perimeter_of_polygons-311"><a href="#perimeter_of_polygons-311"><span class="linenos">311</span></a><span class="sd">    | --- | --- |</span>
@@ -1579,7 +1580,7 @@
 </span><span id="perimeter_of_polygons-314"><a href="#perimeter_of_polygons-314"><span class="linenos">314</span></a>    <span class="n">size_of_sides</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">max_sides</span><span class="p">)</span>
 </span><span id="perimeter_of_polygons-315"><a href="#perimeter_of_polygons-315"><span class="linenos">315</span></a>    <span class="n">sides</span> <span class="o">=</span> <span class="p">[</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_length</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">size_of_sides</span><span class="p">)]</span>
 </span><span id="perimeter_of_polygons-316"><a href="#perimeter_of_polygons-316"><span class="linenos">316</span></a>
-</span><span id="perimeter_of_polygons-317"><a href="#perimeter_of_polygons-317"><span class="linenos">317</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;The perimeter of a $</span><span class="si">{</span><span class="n">size_of_sides</span><span class="si">}</span><span class="s2">$ sided polygon with lengths of $</span><span class="si">{</span><span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="n">sides</span><span class="p">))</span><span class="si">}</span><span class="s2">$cm is: &quot;</span>
+</span><span id="perimeter_of_polygons-317"><a href="#perimeter_of_polygons-317"><span class="linenos">317</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;The perimeter of a $</span><span class="si">{</span><span class="n">size_of_sides</span><span class="si">}</span><span class="s2">$ sided polygon with lengths of $</span><span class="si">{</span><span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span><span class="w"> </span><span class="n">sides</span><span class="p">))</span><span class="si">}</span><span class="s2">$cm is: &quot;</span>
 </span><span id="perimeter_of_polygons-318"><a href="#perimeter_of_polygons-318"><span class="linenos">318</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">sides</span><span class="p">)</span>
 </span><span id="perimeter_of_polygons-319"><a href="#perimeter_of_polygons-319"><span class="linenos">319</span></a>
 </span><span id="perimeter_of_polygons-320"><a href="#perimeter_of_polygons-320"><span class="linenos">320</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="n">solution</span><span class="si">}</span><span class="s1">$&#39;</span>
@@ -1618,7 +1619,7 @@
     </div>
     <a class="headerlink" href="#pythagorean_theorem"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="pythagorean_theorem-323"><a href="#pythagorean_theorem-323"><span class="linenos">323</span></a><span class="k">def</span> <span class="nf">pythagorean_theorem</span><span class="p">(</span><span class="n">max_length</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="pythagorean_theorem-324"><a href="#pythagorean_theorem-324"><span class="linenos">324</span></a>    <span class="sd">&quot;&quot;&quot;Pythagorean Theorem</span>
+</span><span id="pythagorean_theorem-324"><a href="#pythagorean_theorem-324"><span class="linenos">324</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Pythagorean Theorem</span>
 </span><span id="pythagorean_theorem-325"><a href="#pythagorean_theorem-325"><span class="linenos">325</span></a>
 </span><span id="pythagorean_theorem-326"><a href="#pythagorean_theorem-326"><span class="linenos">326</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="pythagorean_theorem-327"><a href="#pythagorean_theorem-327"><span class="linenos">327</span></a><span class="sd">    | --- | --- |</span>
@@ -1666,7 +1667,7 @@
     </div>
     <a class="headerlink" href="#radian_to_deg"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="radian_to_deg-339"><a href="#radian_to_deg-339"><span class="linenos">339</span></a><span class="k">def</span> <span class="nf">radian_to_deg</span><span class="p">(</span><span class="n">max_rad</span><span class="o">=</span><span class="mf">6.28</span><span class="p">):</span>
-</span><span id="radian_to_deg-340"><a href="#radian_to_deg-340"><span class="linenos">340</span></a>    <span class="sd">&quot;&quot;&quot;Radians to Degrees&quot;&quot;&quot;</span>
+</span><span id="radian_to_deg-340"><a href="#radian_to_deg-340"><span class="linenos">340</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Radians to Degrees&quot;&quot;&quot;</span>
 </span><span id="radian_to_deg-341"><a href="#radian_to_deg-341"><span class="linenos">341</span></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">int</span><span class="p">(</span><span class="n">max_rad</span> <span class="o">*</span> <span class="mi">100</span><span class="p">))</span> <span class="o">/</span> <span class="mi">100</span>
 </span><span id="radian_to_deg-342"><a href="#radian_to_deg-342"><span class="linenos">342</span></a>    <span class="n">b</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="mi">180</span> <span class="o">*</span> <span class="n">a</span><span class="p">)</span> <span class="o">/</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
 </span><span id="radian_to_deg-343"><a href="#radian_to_deg-343"><span class="linenos">343</span></a>
@@ -1693,7 +1694,7 @@
     </div>
     <a class="headerlink" href="#sector_area"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="sector_area-349"><a href="#sector_area-349"><span class="linenos">349</span></a><span class="k">def</span> <span class="nf">sector_area</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">49</span><span class="p">,</span> <span class="n">max_angle</span><span class="o">=</span><span class="mi">359</span><span class="p">):</span>
-</span><span id="sector_area-350"><a href="#sector_area-350"><span class="linenos">350</span></a>    <span class="sd">&quot;&quot;&quot;Area of a Sector</span>
+</span><span id="sector_area-350"><a href="#sector_area-350"><span class="linenos">350</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Area of a Sector</span>
 </span><span id="sector_area-351"><a href="#sector_area-351"><span class="linenos">351</span></a>
 </span><span id="sector_area-352"><a href="#sector_area-352"><span class="linenos">352</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="sector_area-353"><a href="#sector_area-353"><span class="linenos">353</span></a><span class="sd">    | --- | --- |</span>
@@ -1742,7 +1743,7 @@
     </div>
     <a class="headerlink" href="#sum_of_polygon_angles"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="sum_of_polygon_angles-366"><a href="#sum_of_polygon_angles-366"><span class="linenos">366</span></a><span class="k">def</span> <span class="nf">sum_of_polygon_angles</span><span class="p">(</span><span class="n">max_sides</span><span class="o">=</span><span class="mi">12</span><span class="p">):</span>
-</span><span id="sum_of_polygon_angles-367"><a href="#sum_of_polygon_angles-367"><span class="linenos">367</span></a>    <span class="sd">&quot;&quot;&quot;Sum of Angles of Polygon</span>
+</span><span id="sum_of_polygon_angles-367"><a href="#sum_of_polygon_angles-367"><span class="linenos">367</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Sum of Angles of Polygon</span>
 </span><span id="sum_of_polygon_angles-368"><a href="#sum_of_polygon_angles-368"><span class="linenos">368</span></a>
 </span><span id="sum_of_polygon_angles-369"><a href="#sum_of_polygon_angles-369"><span class="linenos">369</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="sum_of_polygon_angles-370"><a href="#sum_of_polygon_angles-370"><span class="linenos">370</span></a><span class="sd">    | --- | --- |</span>
@@ -1788,7 +1789,7 @@
     </div>
     <a class="headerlink" href="#surface_area_cone"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="surface_area_cone-380"><a href="#surface_area_cone-380"><span class="linenos">380</span></a><span class="k">def</span> <span class="nf">surface_area_cone</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_height</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="surface_area_cone-381"><a href="#surface_area_cone-381"><span class="linenos">381</span></a>    <span class="sd">&quot;&quot;&quot;Surface area of a cone</span>
+</span><span id="surface_area_cone-381"><a href="#surface_area_cone-381"><span class="linenos">381</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Surface area of a cone</span>
 </span><span id="surface_area_cone-382"><a href="#surface_area_cone-382"><span class="linenos">382</span></a>
 </span><span id="surface_area_cone-383"><a href="#surface_area_cone-383"><span class="linenos">383</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="surface_area_cone-384"><a href="#surface_area_cone-384"><span class="linenos">384</span></a><span class="sd">    | --- | --- |</span>
@@ -1838,7 +1839,7 @@
     </div>
     <a class="headerlink" href="#surface_area_cube"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="surface_area_cube-398"><a href="#surface_area_cube-398"><span class="linenos">398</span></a><span class="k">def</span> <span class="nf">surface_area_cube</span><span class="p">(</span><span class="n">max_side</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="surface_area_cube-399"><a href="#surface_area_cube-399"><span class="linenos">399</span></a>    <span class="sd">&quot;&quot;&quot;Surface area of a cube</span>
+</span><span id="surface_area_cube-399"><a href="#surface_area_cube-399"><span class="linenos">399</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Surface area of a cube</span>
 </span><span id="surface_area_cube-400"><a href="#surface_area_cube-400"><span class="linenos">400</span></a>
 </span><span id="surface_area_cube-401"><a href="#surface_area_cube-401"><span class="linenos">401</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="surface_area_cube-402"><a href="#surface_area_cube-402"><span class="linenos">402</span></a><span class="sd">    | --- | --- |</span>
@@ -1885,7 +1886,7 @@
     </div>
     <a class="headerlink" href="#surface_area_cuboid"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="surface_area_cuboid-413"><a href="#surface_area_cuboid-413"><span class="linenos">413</span></a><span class="k">def</span> <span class="nf">surface_area_cuboid</span><span class="p">(</span><span class="n">max_side</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="surface_area_cuboid-414"><a href="#surface_area_cuboid-414"><span class="linenos">414</span></a>    <span class="sd">&quot;&quot;&quot;Surface area of a cuboid</span>
+</span><span id="surface_area_cuboid-414"><a href="#surface_area_cuboid-414"><span class="linenos">414</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Surface area of a cuboid</span>
 </span><span id="surface_area_cuboid-415"><a href="#surface_area_cuboid-415"><span class="linenos">415</span></a>
 </span><span id="surface_area_cuboid-416"><a href="#surface_area_cuboid-416"><span class="linenos">416</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="surface_area_cuboid-417"><a href="#surface_area_cuboid-417"><span class="linenos">417</span></a><span class="sd">    | --- | --- |</span>
@@ -1934,7 +1935,7 @@
     </div>
     <a class="headerlink" href="#surface_area_cylinder"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="surface_area_cylinder-430"><a href="#surface_area_cylinder-430"><span class="linenos">430</span></a><span class="k">def</span> <span class="nf">surface_area_cylinder</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_height</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="surface_area_cylinder-431"><a href="#surface_area_cylinder-431"><span class="linenos">431</span></a>    <span class="sd">&quot;&quot;&quot;Surface area of a cylinder</span>
+</span><span id="surface_area_cylinder-431"><a href="#surface_area_cylinder-431"><span class="linenos">431</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Surface area of a cylinder</span>
 </span><span id="surface_area_cylinder-432"><a href="#surface_area_cylinder-432"><span class="linenos">432</span></a>
 </span><span id="surface_area_cylinder-433"><a href="#surface_area_cylinder-433"><span class="linenos">433</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="surface_area_cylinder-434"><a href="#surface_area_cylinder-434"><span class="linenos">434</span></a><span class="sd">    | --- | --- |</span>
@@ -1982,7 +1983,7 @@
     </div>
     <a class="headerlink" href="#surface_area_pyramid"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="surface_area_pyramid-446"><a href="#surface_area_pyramid-446"><span class="linenos">446</span></a><span class="k">def</span> <span class="nf">surface_area_pyramid</span><span class="p">(</span><span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="surface_area_pyramid-447"><a href="#surface_area_pyramid-447"><span class="linenos">447</span></a>    <span class="sd">&quot;&quot;&quot;Surface area of a pyramid</span>
+</span><span id="surface_area_pyramid-447"><a href="#surface_area_pyramid-447"><span class="linenos">447</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Surface area of a pyramid</span>
 </span><span id="surface_area_pyramid-448"><a href="#surface_area_pyramid-448"><span class="linenos">448</span></a>
 </span><span id="surface_area_pyramid-449"><a href="#surface_area_pyramid-449"><span class="linenos">449</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="surface_area_pyramid-450"><a href="#surface_area_pyramid-450"><span class="linenos">450</span></a><span class="sd">    | --- | --- |</span>
@@ -2056,7 +2057,7 @@
     </div>
     <a class="headerlink" href="#surface_area_sphere"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="surface_area_sphere-488"><a href="#surface_area_sphere-488"><span class="linenos">488</span></a><span class="k">def</span> <span class="nf">surface_area_sphere</span><span class="p">(</span><span class="n">max_side</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="surface_area_sphere-489"><a href="#surface_area_sphere-489"><span class="linenos">489</span></a>    <span class="sd">&quot;&quot;&quot;Surface area of a sphere</span>
+</span><span id="surface_area_sphere-489"><a href="#surface_area_sphere-489"><span class="linenos">489</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Surface area of a sphere</span>
 </span><span id="surface_area_sphere-490"><a href="#surface_area_sphere-490"><span class="linenos">490</span></a>
 </span><span id="surface_area_sphere-491"><a href="#surface_area_sphere-491"><span class="linenos">491</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="surface_area_sphere-492"><a href="#surface_area_sphere-492"><span class="linenos">492</span></a><span class="sd">    | --- | --- |</span>
@@ -2103,7 +2104,7 @@
     </div>
     <a class="headerlink" href="#third_angle_of_triangle"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="third_angle_of_triangle-503"><a href="#third_angle_of_triangle-503"><span class="linenos">503</span></a><span class="k">def</span> <span class="nf">third_angle_of_triangle</span><span class="p">(</span><span class="n">max_angle</span><span class="o">=</span><span class="mi">89</span><span class="p">):</span>
-</span><span id="third_angle_of_triangle-504"><a href="#third_angle_of_triangle-504"><span class="linenos">504</span></a>    <span class="sd">&quot;&quot;&quot;Third Angle of Triangle</span>
+</span><span id="third_angle_of_triangle-504"><a href="#third_angle_of_triangle-504"><span class="linenos">504</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Third Angle of Triangle</span>
 </span><span id="third_angle_of_triangle-505"><a href="#third_angle_of_triangle-505"><span class="linenos">505</span></a>
 </span><span id="third_angle_of_triangle-506"><a href="#third_angle_of_triangle-506"><span class="linenos">506</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="third_angle_of_triangle-507"><a href="#third_angle_of_triangle-507"><span class="linenos">507</span></a><span class="sd">    | --- | --- |</span>
@@ -2150,7 +2151,7 @@
     </div>
     <a class="headerlink" href="#valid_triangle"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="valid_triangle-518"><a href="#valid_triangle-518"><span class="linenos">518</span></a><span class="k">def</span> <span class="nf">valid_triangle</span><span class="p">(</span><span class="n">max_side_length</span><span class="o">=</span><span class="mi">50</span><span class="p">):</span>
-</span><span id="valid_triangle-519"><a href="#valid_triangle-519"><span class="linenos">519</span></a>    <span class="sd">&quot;&quot;&quot;Valid Triangle</span>
+</span><span id="valid_triangle-519"><a href="#valid_triangle-519"><span class="linenos">519</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Valid Triangle</span>
 </span><span id="valid_triangle-520"><a href="#valid_triangle-520"><span class="linenos">520</span></a>
 </span><span id="valid_triangle-521"><a href="#valid_triangle-521"><span class="linenos">521</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="valid_triangle-522"><a href="#valid_triangle-522"><span class="linenos">522</span></a><span class="sd">    | --- | --- |</span>
@@ -2204,7 +2205,7 @@
     </div>
     <a class="headerlink" href="#volume_cone"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="volume_cone-540"><a href="#volume_cone-540"><span class="linenos">540</span></a><span class="k">def</span> <span class="nf">volume_cone</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_height</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="volume_cone-541"><a href="#volume_cone-541"><span class="linenos">541</span></a>    <span class="sd">&quot;&quot;&quot;Volume of a cone</span>
+</span><span id="volume_cone-541"><a href="#volume_cone-541"><span class="linenos">541</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Volume of a cone</span>
 </span><span id="volume_cone-542"><a href="#volume_cone-542"><span class="linenos">542</span></a>
 </span><span id="volume_cone-543"><a href="#volume_cone-543"><span class="linenos">543</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="volume_cone-544"><a href="#volume_cone-544"><span class="linenos">544</span></a><span class="sd">    | --- | --- |</span>
@@ -2252,24 +2253,37 @@
     </div>
     <a class="headerlink" href="#volume_cube"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="volume_cube-556"><a href="#volume_cube-556"><span class="linenos">556</span></a><span class="k">def</span> <span class="nf">volume_cube</span><span class="p">(</span><span class="n">max_side</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="volume_cube-557"><a href="#volume_cube-557"><span class="linenos">557</span></a>    <span class="sd">&quot;&quot;&quot;Volume of a cube</span>
-</span><span id="volume_cube-558"><a href="#volume_cube-558"><span class="linenos">558</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
-</span><span id="volume_cube-559"><a href="#volume_cube-559"><span class="linenos">559</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="volume_cube-560"><a href="#volume_cube-560"><span class="linenos">560</span></a><span class="sd">    | Volume of a cube with a side length of $19m$ is | $6859 m^3$ |</span>
-</span><span id="volume_cube-561"><a href="#volume_cube-561"><span class="linenos">561</span></a><span class="sd">    &quot;&quot;&quot;</span>
-</span><span id="volume_cube-562"><a href="#volume_cube-562"><span class="linenos">562</span></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_side</span><span class="p">)</span>
-</span><span id="volume_cube-563"><a href="#volume_cube-563"><span class="linenos">563</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="n">a</span><span class="o">**</span><span class="mi">3</span>
-</span><span id="volume_cube-564"><a href="#volume_cube-564"><span class="linenos">564</span></a>
-</span><span id="volume_cube-565"><a href="#volume_cube-565"><span class="linenos">565</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of cube with a side length of $</span><span class="si">{</span><span class="n">a</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is&quot;</span>
-</span><span id="volume_cube-566"><a href="#volume_cube-566"><span class="linenos">566</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">^3$&quot;</span>
-</span><span id="volume_cube-567"><a href="#volume_cube-567"><span class="linenos">567</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
+</span><span id="volume_cube-557"><a href="#volume_cube-557"><span class="linenos">557</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Volume of a cube</span>
+</span><span id="volume_cube-558"><a href="#volume_cube-558"><span class="linenos">558</span></a><span class="sd">    </span>
+</span><span id="volume_cube-559"><a href="#volume_cube-559"><span class="linenos">559</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
+</span><span id="volume_cube-560"><a href="#volume_cube-560"><span class="linenos">560</span></a><span class="sd">    | --- | --- |</span>
+</span><span id="volume_cube-561"><a href="#volume_cube-561"><span class="linenos">561</span></a><span class="sd">    | Volume of a cube with a side length of $19m$ is | $6859 m^3$ |</span>
+</span><span id="volume_cube-562"><a href="#volume_cube-562"><span class="linenos">562</span></a><span class="sd">    &quot;&quot;&quot;</span>
+</span><span id="volume_cube-563"><a href="#volume_cube-563"><span class="linenos">563</span></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_side</span><span class="p">)</span>
+</span><span id="volume_cube-564"><a href="#volume_cube-564"><span class="linenos">564</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="n">a</span><span class="o">**</span><span class="mi">3</span>
+</span><span id="volume_cube-565"><a href="#volume_cube-565"><span class="linenos">565</span></a>
+</span><span id="volume_cube-566"><a href="#volume_cube-566"><span class="linenos">566</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of cube with a side length of $</span><span class="si">{</span><span class="n">a</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is&quot;</span>
+</span><span id="volume_cube-567"><a href="#volume_cube-567"><span class="linenos">567</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">^3$&quot;</span>
+</span><span id="volume_cube-568"><a href="#volume_cube-568"><span class="linenos">568</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span></pre></div>
 
 
-            <div class="docstring"><p>Volume of a cube
-| Ex. Problem | Ex. Solution |
-| --- | --- |
-| Volume of a cube with a side length of $19m$ is | $6859 m^3$ |</p>
+            <div class="docstring"><p>Volume of a cube</p>
+
+<table>
+<thead>
+<tr>
+  <th>Ex. Problem</th>
+  <th>Ex. Solution</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+  <td>Volume of a cube with a side length of $19m$ is</td>
+  <td>$6859 m^3$</td>
+</tr>
+</tbody>
+</table>
 </div>
 
 
@@ -2285,21 +2299,21 @@
 
     </div>
     <a class="headerlink" href="#volume_cuboid"></a>
-            <div class="pdoc-code codehilite"><pre><span></span><span id="volume_cuboid-570"><a href="#volume_cuboid-570"><span class="linenos">570</span></a><span class="k">def</span> <span class="nf">volume_cuboid</span><span class="p">(</span><span class="n">max_side</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="volume_cuboid-571"><a href="#volume_cuboid-571"><span class="linenos">571</span></a>    <span class="sd">&quot;&quot;&quot;Volume of a cuboid</span>
-</span><span id="volume_cuboid-572"><a href="#volume_cuboid-572"><span class="linenos">572</span></a>
-</span><span id="volume_cuboid-573"><a href="#volume_cuboid-573"><span class="linenos">573</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
-</span><span id="volume_cuboid-574"><a href="#volume_cuboid-574"><span class="linenos">574</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="volume_cuboid-575"><a href="#volume_cuboid-575"><span class="linenos">575</span></a><span class="sd">    | Volume of cuboid with sides = $17m, 11m, 13m$ is | $2431 m^3$ |</span>
-</span><span id="volume_cuboid-576"><a href="#volume_cuboid-576"><span class="linenos">576</span></a><span class="sd">    &quot;&quot;&quot;</span>
-</span><span id="volume_cuboid-577"><a href="#volume_cuboid-577"><span class="linenos">577</span></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_side</span><span class="p">)</span>
-</span><span id="volume_cuboid-578"><a href="#volume_cuboid-578"><span class="linenos">578</span></a>    <span class="n">b</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_side</span><span class="p">)</span>
-</span><span id="volume_cuboid-579"><a href="#volume_cuboid-579"><span class="linenos">579</span></a>    <span class="n">c</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_side</span><span class="p">)</span>
-</span><span id="volume_cuboid-580"><a href="#volume_cuboid-580"><span class="linenos">580</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="n">a</span> <span class="o">*</span> <span class="n">b</span> <span class="o">*</span> <span class="n">c</span>
-</span><span id="volume_cuboid-581"><a href="#volume_cuboid-581"><span class="linenos">581</span></a>
-</span><span id="volume_cuboid-582"><a href="#volume_cuboid-582"><span class="linenos">582</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of cuboid with sides = $</span><span class="si">{</span><span class="n">a</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">, </span><span class="si">{</span><span class="n">b</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">, </span><span class="si">{</span><span class="n">c</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is&quot;</span>
-</span><span id="volume_cuboid-583"><a href="#volume_cuboid-583"><span class="linenos">583</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">^3$&quot;</span>
-</span><span id="volume_cuboid-584"><a href="#volume_cuboid-584"><span class="linenos">584</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
+            <div class="pdoc-code codehilite"><pre><span></span><span id="volume_cuboid-571"><a href="#volume_cuboid-571"><span class="linenos">571</span></a><span class="k">def</span> <span class="nf">volume_cuboid</span><span class="p">(</span><span class="n">max_side</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
+</span><span id="volume_cuboid-572"><a href="#volume_cuboid-572"><span class="linenos">572</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Volume of a cuboid</span>
+</span><span id="volume_cuboid-573"><a href="#volume_cuboid-573"><span class="linenos">573</span></a>
+</span><span id="volume_cuboid-574"><a href="#volume_cuboid-574"><span class="linenos">574</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
+</span><span id="volume_cuboid-575"><a href="#volume_cuboid-575"><span class="linenos">575</span></a><span class="sd">    | --- | --- |</span>
+</span><span id="volume_cuboid-576"><a href="#volume_cuboid-576"><span class="linenos">576</span></a><span class="sd">    | Volume of cuboid with sides = $17m, 11m, 13m$ is | $2431 m^3$ |</span>
+</span><span id="volume_cuboid-577"><a href="#volume_cuboid-577"><span class="linenos">577</span></a><span class="sd">    &quot;&quot;&quot;</span>
+</span><span id="volume_cuboid-578"><a href="#volume_cuboid-578"><span class="linenos">578</span></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_side</span><span class="p">)</span>
+</span><span id="volume_cuboid-579"><a href="#volume_cuboid-579"><span class="linenos">579</span></a>    <span class="n">b</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_side</span><span class="p">)</span>
+</span><span id="volume_cuboid-580"><a href="#volume_cuboid-580"><span class="linenos">580</span></a>    <span class="n">c</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_side</span><span class="p">)</span>
+</span><span id="volume_cuboid-581"><a href="#volume_cuboid-581"><span class="linenos">581</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="n">a</span> <span class="o">*</span> <span class="n">b</span> <span class="o">*</span> <span class="n">c</span>
+</span><span id="volume_cuboid-582"><a href="#volume_cuboid-582"><span class="linenos">582</span></a>
+</span><span id="volume_cuboid-583"><a href="#volume_cuboid-583"><span class="linenos">583</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of cuboid with sides = $</span><span class="si">{</span><span class="n">a</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">, </span><span class="si">{</span><span class="n">b</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">, </span><span class="si">{</span><span class="n">c</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is&quot;</span>
+</span><span id="volume_cuboid-584"><a href="#volume_cuboid-584"><span class="linenos">584</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">^3$&quot;</span>
+</span><span id="volume_cuboid-585"><a href="#volume_cuboid-585"><span class="linenos">585</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span></pre></div>
 
 
@@ -2334,20 +2348,20 @@
 
     </div>
     <a class="headerlink" href="#volume_cylinder"></a>
-            <div class="pdoc-code codehilite"><pre><span></span><span id="volume_cylinder-587"><a href="#volume_cylinder-587"><span class="linenos">587</span></a><span class="k">def</span> <span class="nf">volume_cylinder</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_height</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="volume_cylinder-588"><a href="#volume_cylinder-588"><span class="linenos">588</span></a>    <span class="sd">&quot;&quot;&quot;Volume of a cylinder</span>
-</span><span id="volume_cylinder-589"><a href="#volume_cylinder-589"><span class="linenos">589</span></a>
-</span><span id="volume_cylinder-590"><a href="#volume_cylinder-590"><span class="linenos">590</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
-</span><span id="volume_cylinder-591"><a href="#volume_cylinder-591"><span class="linenos">591</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="volume_cylinder-592"><a href="#volume_cylinder-592"><span class="linenos">592</span></a><span class="sd">    | Volume of cylinder with height $= 3m$ and radius $= 10m$ is | $942 m^3$ |</span>
-</span><span id="volume_cylinder-593"><a href="#volume_cylinder-593"><span class="linenos">593</span></a><span class="sd">    &quot;&quot;&quot;</span>
-</span><span id="volume_cylinder-594"><a href="#volume_cylinder-594"><span class="linenos">594</span></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_height</span><span class="p">)</span>
-</span><span id="volume_cylinder-595"><a href="#volume_cylinder-595"><span class="linenos">595</span></a>    <span class="n">b</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_radius</span><span class="p">)</span>
-</span><span id="volume_cylinder-596"><a href="#volume_cylinder-596"><span class="linenos">596</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">b</span> <span class="o">*</span> <span class="n">b</span> <span class="o">*</span> <span class="n">a</span><span class="p">)</span>
-</span><span id="volume_cylinder-597"><a href="#volume_cylinder-597"><span class="linenos">597</span></a>
-</span><span id="volume_cylinder-598"><a href="#volume_cylinder-598"><span class="linenos">598</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of cylinder with height $= </span><span class="si">{</span><span class="n">a</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ and radius $= </span><span class="si">{</span><span class="n">b</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is&quot;</span>
-</span><span id="volume_cylinder-599"><a href="#volume_cylinder-599"><span class="linenos">599</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">^3$&quot;</span>
-</span><span id="volume_cylinder-600"><a href="#volume_cylinder-600"><span class="linenos">600</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
+            <div class="pdoc-code codehilite"><pre><span></span><span id="volume_cylinder-588"><a href="#volume_cylinder-588"><span class="linenos">588</span></a><span class="k">def</span> <span class="nf">volume_cylinder</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_height</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
+</span><span id="volume_cylinder-589"><a href="#volume_cylinder-589"><span class="linenos">589</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Volume of a cylinder</span>
+</span><span id="volume_cylinder-590"><a href="#volume_cylinder-590"><span class="linenos">590</span></a>
+</span><span id="volume_cylinder-591"><a href="#volume_cylinder-591"><span class="linenos">591</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
+</span><span id="volume_cylinder-592"><a href="#volume_cylinder-592"><span class="linenos">592</span></a><span class="sd">    | --- | --- |</span>
+</span><span id="volume_cylinder-593"><a href="#volume_cylinder-593"><span class="linenos">593</span></a><span class="sd">    | Volume of cylinder with height $= 3m$ and radius $= 10m$ is | $942 m^3$ |</span>
+</span><span id="volume_cylinder-594"><a href="#volume_cylinder-594"><span class="linenos">594</span></a><span class="sd">    &quot;&quot;&quot;</span>
+</span><span id="volume_cylinder-595"><a href="#volume_cylinder-595"><span class="linenos">595</span></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_height</span><span class="p">)</span>
+</span><span id="volume_cylinder-596"><a href="#volume_cylinder-596"><span class="linenos">596</span></a>    <span class="n">b</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_radius</span><span class="p">)</span>
+</span><span id="volume_cylinder-597"><a href="#volume_cylinder-597"><span class="linenos">597</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">b</span> <span class="o">*</span> <span class="n">b</span> <span class="o">*</span> <span class="n">a</span><span class="p">)</span>
+</span><span id="volume_cylinder-598"><a href="#volume_cylinder-598"><span class="linenos">598</span></a>
+</span><span id="volume_cylinder-599"><a href="#volume_cylinder-599"><span class="linenos">599</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of cylinder with height $= </span><span class="si">{</span><span class="n">a</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ and radius $= </span><span class="si">{</span><span class="n">b</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is&quot;</span>
+</span><span id="volume_cylinder-600"><a href="#volume_cylinder-600"><span class="linenos">600</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">^3$&quot;</span>
+</span><span id="volume_cylinder-601"><a href="#volume_cylinder-601"><span class="linenos">601</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span></pre></div>
 
 
@@ -2382,21 +2396,21 @@
 
     </div>
     <a class="headerlink" href="#volume_cone_frustum"></a>
-            <div class="pdoc-code codehilite"><pre><span></span><span id="volume_cone_frustum-603"><a href="#volume_cone_frustum-603"><span class="linenos">603</span></a><span class="k">def</span> <span class="nf">volume_cone_frustum</span><span class="p">(</span><span class="n">max_r1</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_r2</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_height</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="volume_cone_frustum-604"><a href="#volume_cone_frustum-604"><span class="linenos">604</span></a>    <span class="sd">&quot;&quot;&quot;Volume of the frustum of a cone</span>
-</span><span id="volume_cone_frustum-605"><a href="#volume_cone_frustum-605"><span class="linenos">605</span></a>
-</span><span id="volume_cone_frustum-606"><a href="#volume_cone_frustum-606"><span class="linenos">606</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
-</span><span id="volume_cone_frustum-607"><a href="#volume_cone_frustum-607"><span class="linenos">607</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="volume_cone_frustum-608"><a href="#volume_cone_frustum-608"><span class="linenos">608</span></a><span class="sd">    | Volume of frustum with height $= 30m$ and $r1 = 20m$ is and $r2 = 8m$ is | $19603.54 m^3$ |</span>
-</span><span id="volume_cone_frustum-609"><a href="#volume_cone_frustum-609"><span class="linenos">609</span></a><span class="sd">    &quot;&quot;&quot;</span>
-</span><span id="volume_cone_frustum-610"><a href="#volume_cone_frustum-610"><span class="linenos">610</span></a>    <span class="n">h</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_height</span><span class="p">)</span>
-</span><span id="volume_cone_frustum-611"><a href="#volume_cone_frustum-611"><span class="linenos">611</span></a>    <span class="n">r1</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_r1</span><span class="p">)</span>
-</span><span id="volume_cone_frustum-612"><a href="#volume_cone_frustum-612"><span class="linenos">612</span></a>    <span class="n">r2</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_r2</span><span class="p">)</span>
-</span><span id="volume_cone_frustum-613"><a href="#volume_cone_frustum-613"><span class="linenos">613</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(((</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">h</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">r1</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">r2</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">r1</span> <span class="o">*</span> <span class="n">r2</span><span class="p">))</span> <span class="o">/</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-</span><span id="volume_cone_frustum-614"><a href="#volume_cone_frustum-614"><span class="linenos">614</span></a>
-</span><span id="volume_cone_frustum-615"><a href="#volume_cone_frustum-615"><span class="linenos">615</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of frustum with height $= </span><span class="si">{</span><span class="n">h</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ and $r1 = </span><span class="si">{</span><span class="n">r1</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is and $r2 = </span><span class="si">{</span><span class="n">r2</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is &quot;</span>
-</span><span id="volume_cone_frustum-616"><a href="#volume_cone_frustum-616"><span class="linenos">616</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">^3$&quot;</span>
-</span><span id="volume_cone_frustum-617"><a href="#volume_cone_frustum-617"><span class="linenos">617</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
+            <div class="pdoc-code codehilite"><pre><span></span><span id="volume_cone_frustum-604"><a href="#volume_cone_frustum-604"><span class="linenos">604</span></a><span class="k">def</span> <span class="nf">volume_cone_frustum</span><span class="p">(</span><span class="n">max_r1</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_r2</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_height</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
+</span><span id="volume_cone_frustum-605"><a href="#volume_cone_frustum-605"><span class="linenos">605</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Volume of the frustum of a cone</span>
+</span><span id="volume_cone_frustum-606"><a href="#volume_cone_frustum-606"><span class="linenos">606</span></a>
+</span><span id="volume_cone_frustum-607"><a href="#volume_cone_frustum-607"><span class="linenos">607</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
+</span><span id="volume_cone_frustum-608"><a href="#volume_cone_frustum-608"><span class="linenos">608</span></a><span class="sd">    | --- | --- |</span>
+</span><span id="volume_cone_frustum-609"><a href="#volume_cone_frustum-609"><span class="linenos">609</span></a><span class="sd">    | Volume of frustum with height $= 30m$ and $r1 = 20m$ is and $r2 = 8m$ is | $19603.54 m^3$ |</span>
+</span><span id="volume_cone_frustum-610"><a href="#volume_cone_frustum-610"><span class="linenos">610</span></a><span class="sd">    &quot;&quot;&quot;</span>
+</span><span id="volume_cone_frustum-611"><a href="#volume_cone_frustum-611"><span class="linenos">611</span></a>    <span class="n">h</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_height</span><span class="p">)</span>
+</span><span id="volume_cone_frustum-612"><a href="#volume_cone_frustum-612"><span class="linenos">612</span></a>    <span class="n">r1</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_r1</span><span class="p">)</span>
+</span><span id="volume_cone_frustum-613"><a href="#volume_cone_frustum-613"><span class="linenos">613</span></a>    <span class="n">r2</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_r2</span><span class="p">)</span>
+</span><span id="volume_cone_frustum-614"><a href="#volume_cone_frustum-614"><span class="linenos">614</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(((</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">h</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">r1</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">r2</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">r1</span> <span class="o">*</span> <span class="n">r2</span><span class="p">))</span> <span class="o">/</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
+</span><span id="volume_cone_frustum-615"><a href="#volume_cone_frustum-615"><span class="linenos">615</span></a>
+</span><span id="volume_cone_frustum-616"><a href="#volume_cone_frustum-616"><span class="linenos">616</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of frustum with height $= </span><span class="si">{</span><span class="n">h</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ and $r1 = </span><span class="si">{</span><span class="n">r1</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is and $r2 = </span><span class="si">{</span><span class="n">r2</span><span class="si">}{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is &quot;</span>
+</span><span id="volume_cone_frustum-617"><a href="#volume_cone_frustum-617"><span class="linenos">617</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">^3$&quot;</span>
+</span><span id="volume_cone_frustum-618"><a href="#volume_cone_frustum-618"><span class="linenos">618</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span></pre></div>
 
 
@@ -2431,19 +2445,19 @@
 
     </div>
     <a class="headerlink" href="#volume_hemisphere"></a>
-            <div class="pdoc-code codehilite"><pre><span></span><span id="volume_hemisphere-620"><a href="#volume_hemisphere-620"><span class="linenos">620</span></a><span class="k">def</span> <span class="nf">volume_hemisphere</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="volume_hemisphere-621"><a href="#volume_hemisphere-621"><span class="linenos">621</span></a>    <span class="sd">&quot;&quot;&quot;Volume of a hemisphere</span>
-</span><span id="volume_hemisphere-622"><a href="#volume_hemisphere-622"><span class="linenos">622</span></a>
-</span><span id="volume_hemisphere-623"><a href="#volume_hemisphere-623"><span class="linenos">623</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
-</span><span id="volume_hemisphere-624"><a href="#volume_hemisphere-624"><span class="linenos">624</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="volume_hemisphere-625"><a href="#volume_hemisphere-625"><span class="linenos">625</span></a><span class="sd">    | Volume of hemisphere with radius $32m =$ | $68629.14 m^3$ |</span>
-</span><span id="volume_hemisphere-626"><a href="#volume_hemisphere-626"><span class="linenos">626</span></a><span class="sd">    &quot;&quot;&quot;</span>
-</span><span id="volume_hemisphere-627"><a href="#volume_hemisphere-627"><span class="linenos">627</span></a>    <span class="n">r</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_radius</span><span class="p">)</span>
-</span><span id="volume_hemisphere-628"><a href="#volume_hemisphere-628"><span class="linenos">628</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="mi">2</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span> <span class="o">/</span> <span class="mi">3</span><span class="p">)</span> <span class="o">*</span> <span class="n">r</span><span class="o">**</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-</span><span id="volume_hemisphere-629"><a href="#volume_hemisphere-629"><span class="linenos">629</span></a>
-</span><span id="volume_hemisphere-630"><a href="#volume_hemisphere-630"><span class="linenos">630</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of hemisphere with radius $</span><span class="si">{</span><span class="n">r</span><span class="si">}</span><span class="s2"> m =$ &quot;</span>
-</span><span id="volume_hemisphere-631"><a href="#volume_hemisphere-631"><span class="linenos">631</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> m^3$&quot;</span>
-</span><span id="volume_hemisphere-632"><a href="#volume_hemisphere-632"><span class="linenos">632</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
+            <div class="pdoc-code codehilite"><pre><span></span><span id="volume_hemisphere-621"><a href="#volume_hemisphere-621"><span class="linenos">621</span></a><span class="k">def</span> <span class="nf">volume_hemisphere</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
+</span><span id="volume_hemisphere-622"><a href="#volume_hemisphere-622"><span class="linenos">622</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Volume of a hemisphere</span>
+</span><span id="volume_hemisphere-623"><a href="#volume_hemisphere-623"><span class="linenos">623</span></a>
+</span><span id="volume_hemisphere-624"><a href="#volume_hemisphere-624"><span class="linenos">624</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
+</span><span id="volume_hemisphere-625"><a href="#volume_hemisphere-625"><span class="linenos">625</span></a><span class="sd">    | --- | --- |</span>
+</span><span id="volume_hemisphere-626"><a href="#volume_hemisphere-626"><span class="linenos">626</span></a><span class="sd">    | Volume of hemisphere with radius $32m =$ | $68629.14 m^3$ |</span>
+</span><span id="volume_hemisphere-627"><a href="#volume_hemisphere-627"><span class="linenos">627</span></a><span class="sd">    &quot;&quot;&quot;</span>
+</span><span id="volume_hemisphere-628"><a href="#volume_hemisphere-628"><span class="linenos">628</span></a>    <span class="n">r</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_radius</span><span class="p">)</span>
+</span><span id="volume_hemisphere-629"><a href="#volume_hemisphere-629"><span class="linenos">629</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="mi">2</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span> <span class="o">/</span> <span class="mi">3</span><span class="p">)</span> <span class="o">*</span> <span class="n">r</span><span class="o">**</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
+</span><span id="volume_hemisphere-630"><a href="#volume_hemisphere-630"><span class="linenos">630</span></a>
+</span><span id="volume_hemisphere-631"><a href="#volume_hemisphere-631"><span class="linenos">631</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of hemisphere with radius $</span><span class="si">{</span><span class="n">r</span><span class="si">}</span><span class="s2"> m =$ &quot;</span>
+</span><span id="volume_hemisphere-632"><a href="#volume_hemisphere-632"><span class="linenos">632</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> m^3$&quot;</span>
+</span><span id="volume_hemisphere-633"><a href="#volume_hemisphere-633"><span class="linenos">633</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span></pre></div>
 
 
@@ -2478,22 +2492,22 @@
 
     </div>
     <a class="headerlink" href="#volume_pyramid"></a>
-            <div class="pdoc-code codehilite"><pre><span></span><span id="volume_pyramid-635"><a href="#volume_pyramid-635"><span class="linenos">635</span></a><span class="k">def</span> <span class="nf">volume_pyramid</span><span class="p">(</span><span class="n">max_length</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_width</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_height</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
-</span><span id="volume_pyramid-636"><a href="#volume_pyramid-636"><span class="linenos">636</span></a>    <span class="sd">&quot;&quot;&quot;Volume of a pyramid</span>
-</span><span id="volume_pyramid-637"><a href="#volume_pyramid-637"><span class="linenos">637</span></a>
-</span><span id="volume_pyramid-638"><a href="#volume_pyramid-638"><span class="linenos">638</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
-</span><span id="volume_pyramid-639"><a href="#volume_pyramid-639"><span class="linenos">639</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="volume_pyramid-640"><a href="#volume_pyramid-640"><span class="linenos">640</span></a><span class="sd">    | Volume of pyramid with base length $= 7 m$, base width $= 18 m$ and height $= 42 m$ is | $1764.0 m^3$ |</span>
-</span><span id="volume_pyramid-641"><a href="#volume_pyramid-641"><span class="linenos">641</span></a><span class="sd">    &quot;&quot;&quot;</span>
-</span><span id="volume_pyramid-642"><a href="#volume_pyramid-642"><span class="linenos">642</span></a>    <span class="n">length</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_length</span><span class="p">)</span>
-</span><span id="volume_pyramid-643"><a href="#volume_pyramid-643"><span class="linenos">643</span></a>    <span class="n">width</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_width</span><span class="p">)</span>
-</span><span id="volume_pyramid-644"><a href="#volume_pyramid-644"><span class="linenos">644</span></a>    <span class="n">height</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_height</span><span class="p">)</span>
-</span><span id="volume_pyramid-645"><a href="#volume_pyramid-645"><span class="linenos">645</span></a>
-</span><span id="volume_pyramid-646"><a href="#volume_pyramid-646"><span class="linenos">646</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="n">length</span> <span class="o">*</span> <span class="n">width</span> <span class="o">*</span> <span class="n">height</span><span class="p">)</span> <span class="o">/</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-</span><span id="volume_pyramid-647"><a href="#volume_pyramid-647"><span class="linenos">647</span></a>
-</span><span id="volume_pyramid-648"><a href="#volume_pyramid-648"><span class="linenos">648</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of pyramid with base length $= </span><span class="si">{</span><span class="n">length</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$, base width $= </span><span class="si">{</span><span class="n">width</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ and height $= </span><span class="si">{</span><span class="n">height</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is&quot;</span>
-</span><span id="volume_pyramid-649"><a href="#volume_pyramid-649"><span class="linenos">649</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">^3$&quot;</span>
-</span><span id="volume_pyramid-650"><a href="#volume_pyramid-650"><span class="linenos">650</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
+            <div class="pdoc-code codehilite"><pre><span></span><span id="volume_pyramid-636"><a href="#volume_pyramid-636"><span class="linenos">636</span></a><span class="k">def</span> <span class="nf">volume_pyramid</span><span class="p">(</span><span class="n">max_length</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_width</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">max_height</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">&#39;m&#39;</span><span class="p">):</span>
+</span><span id="volume_pyramid-637"><a href="#volume_pyramid-637"><span class="linenos">637</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Volume of a pyramid</span>
+</span><span id="volume_pyramid-638"><a href="#volume_pyramid-638"><span class="linenos">638</span></a>
+</span><span id="volume_pyramid-639"><a href="#volume_pyramid-639"><span class="linenos">639</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
+</span><span id="volume_pyramid-640"><a href="#volume_pyramid-640"><span class="linenos">640</span></a><span class="sd">    | --- | --- |</span>
+</span><span id="volume_pyramid-641"><a href="#volume_pyramid-641"><span class="linenos">641</span></a><span class="sd">    | Volume of pyramid with base length $= 7 m$, base width $= 18 m$ and height $= 42 m$ is | $1764.0 m^3$ |</span>
+</span><span id="volume_pyramid-642"><a href="#volume_pyramid-642"><span class="linenos">642</span></a><span class="sd">    &quot;&quot;&quot;</span>
+</span><span id="volume_pyramid-643"><a href="#volume_pyramid-643"><span class="linenos">643</span></a>    <span class="n">length</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_length</span><span class="p">)</span>
+</span><span id="volume_pyramid-644"><a href="#volume_pyramid-644"><span class="linenos">644</span></a>    <span class="n">width</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_width</span><span class="p">)</span>
+</span><span id="volume_pyramid-645"><a href="#volume_pyramid-645"><span class="linenos">645</span></a>    <span class="n">height</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_height</span><span class="p">)</span>
+</span><span id="volume_pyramid-646"><a href="#volume_pyramid-646"><span class="linenos">646</span></a>
+</span><span id="volume_pyramid-647"><a href="#volume_pyramid-647"><span class="linenos">647</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="n">length</span> <span class="o">*</span> <span class="n">width</span> <span class="o">*</span> <span class="n">height</span><span class="p">)</span> <span class="o">/</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
+</span><span id="volume_pyramid-648"><a href="#volume_pyramid-648"><span class="linenos">648</span></a>
+</span><span id="volume_pyramid-649"><a href="#volume_pyramid-649"><span class="linenos">649</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of pyramid with base length $= </span><span class="si">{</span><span class="n">length</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$, base width $= </span><span class="si">{</span><span class="n">width</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ and height $= </span><span class="si">{</span><span class="n">height</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">$ is&quot;</span>
+</span><span id="volume_pyramid-650"><a href="#volume_pyramid-650"><span class="linenos">650</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">unit</span><span class="si">}</span><span class="s2">^3$&quot;</span>
+</span><span id="volume_pyramid-651"><a href="#volume_pyramid-651"><span class="linenos">651</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span></pre></div>
 
 
@@ -2528,19 +2542,19 @@
 
     </div>
     <a class="headerlink" href="#volume_sphere"></a>
-            <div class="pdoc-code codehilite"><pre><span></span><span id="volume_sphere-653"><a href="#volume_sphere-653"><span class="linenos">653</span></a><span class="k">def</span> <span class="nf">volume_sphere</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="volume_sphere-654"><a href="#volume_sphere-654"><span class="linenos">654</span></a>    <span class="sd">&quot;&quot;&quot;Volume of a sphere</span>
-</span><span id="volume_sphere-655"><a href="#volume_sphere-655"><span class="linenos">655</span></a>
-</span><span id="volume_sphere-656"><a href="#volume_sphere-656"><span class="linenos">656</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
-</span><span id="volume_sphere-657"><a href="#volume_sphere-657"><span class="linenos">657</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="volume_sphere-658"><a href="#volume_sphere-658"><span class="linenos">658</span></a><span class="sd">    | Volume of sphere with radius $30 m = $ | $113097.36 m^3$ |</span>
-</span><span id="volume_sphere-659"><a href="#volume_sphere-659"><span class="linenos">659</span></a><span class="sd">    &quot;&quot;&quot;</span>
-</span><span id="volume_sphere-660"><a href="#volume_sphere-660"><span class="linenos">660</span></a>    <span class="n">r</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_radius</span><span class="p">)</span>
-</span><span id="volume_sphere-661"><a href="#volume_sphere-661"><span class="linenos">661</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="mi">4</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span> <span class="o">/</span> <span class="mi">3</span><span class="p">)</span> <span class="o">*</span> <span class="n">r</span><span class="o">**</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-</span><span id="volume_sphere-662"><a href="#volume_sphere-662"><span class="linenos">662</span></a>
-</span><span id="volume_sphere-663"><a href="#volume_sphere-663"><span class="linenos">663</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of sphere with radius $</span><span class="si">{</span><span class="n">r</span><span class="si">}</span><span class="s2"> m = $&quot;</span>
-</span><span id="volume_sphere-664"><a href="#volume_sphere-664"><span class="linenos">664</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> m^3$&quot;</span>
-</span><span id="volume_sphere-665"><a href="#volume_sphere-665"><span class="linenos">665</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
+            <div class="pdoc-code codehilite"><pre><span></span><span id="volume_sphere-654"><a href="#volume_sphere-654"><span class="linenos">654</span></a><span class="k">def</span> <span class="nf">volume_sphere</span><span class="p">(</span><span class="n">max_radius</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
+</span><span id="volume_sphere-655"><a href="#volume_sphere-655"><span class="linenos">655</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Volume of a sphere</span>
+</span><span id="volume_sphere-656"><a href="#volume_sphere-656"><span class="linenos">656</span></a>
+</span><span id="volume_sphere-657"><a href="#volume_sphere-657"><span class="linenos">657</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
+</span><span id="volume_sphere-658"><a href="#volume_sphere-658"><span class="linenos">658</span></a><span class="sd">    | --- | --- |</span>
+</span><span id="volume_sphere-659"><a href="#volume_sphere-659"><span class="linenos">659</span></a><span class="sd">    | Volume of sphere with radius $30 m = $ | $113097.36 m^3$ |</span>
+</span><span id="volume_sphere-660"><a href="#volume_sphere-660"><span class="linenos">660</span></a><span class="sd">    &quot;&quot;&quot;</span>
+</span><span id="volume_sphere-661"><a href="#volume_sphere-661"><span class="linenos">661</span></a>    <span class="n">r</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_radius</span><span class="p">)</span>
+</span><span id="volume_sphere-662"><a href="#volume_sphere-662"><span class="linenos">662</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="mi">4</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span> <span class="o">/</span> <span class="mi">3</span><span class="p">)</span> <span class="o">*</span> <span class="n">r</span><span class="o">**</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
+</span><span id="volume_sphere-663"><a href="#volume_sphere-663"><span class="linenos">663</span></a>
+</span><span id="volume_sphere-664"><a href="#volume_sphere-664"><span class="linenos">664</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Volume of sphere with radius $</span><span class="si">{</span><span class="n">r</span><span class="si">}</span><span class="s2"> m = $&quot;</span>
+</span><span id="volume_sphere-665"><a href="#volume_sphere-665"><span class="linenos">665</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2"> m^3$&quot;</span>
+</span><span id="volume_sphere-666"><a href="#volume_sphere-666"><span class="linenos">666</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span></pre></div>
 
 
@@ -2684,7 +2698,7 @@
                         if (doc.annotation)
                             heading += `<span class="annotation">${doc.annotation}</span>`;
                         if (doc.default_value)
-                            heading += `<span class="default_value">${doc.default_value}</span>`;
+                            heading += `<span class="default_value"> = ${doc.default_value}</span>`;
                         break;
                     default:
                         heading = `<span class="name">${doc.fullname}</span>`;
diff --git a/docs/mathgenerator/misc.html b/docs/mathgenerator/misc.html
index 3d52752..626c35c 100644
--- a/docs/mathgenerator/misc.html
+++ b/docs/mathgenerator/misc.html
@@ -3,14 +3,14 @@
 <head>
     <meta charset="utf-8">
     <meta name="viewport" content="width=device-width, initial-scale=1">
-    <meta name="generator" content="pdoc 12.3.0"/>
+    <meta name="generator" content="pdoc 13.1.1"/>
     <title>mathgenerator.misc API documentation</title>
 
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@@ -50,8 +50,8 @@
 
 
 
-        <h2>API Documentation</h2>
-            <ul class="memberlist">
+            <h2>API Documentation</h2>
+                <ul class="memberlist">
             <li>
                     <a class="function" href="#arithmetic_progression_sum">arithmetic_progression_sum</a>
             </li>
@@ -153,7 +153,7 @@
 </span><span id="L-6"><a href="#L-6"><span class="linenos">  6</span></a><span class="k">def</span> <span class="nf">arithmetic_progression_sum</span><span class="p">(</span><span class="n">max_d</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
 </span><span id="L-7"><a href="#L-7"><span class="linenos">  7</span></a>                               <span class="n">max_a</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
 </span><span id="L-8"><a href="#L-8"><span class="linenos">  8</span></a>                               <span class="n">max_n</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="L-9"><a href="#L-9"><span class="linenos">  9</span></a>    <span class="sd">&quot;&quot;&quot;Arithmetic Progression Sum</span>
+</span><span id="L-9"><a href="#L-9"><span class="linenos">  9</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Arithmetic Progression Sum</span>
 </span><span id="L-10"><a href="#L-10"><span class="linenos"> 10</span></a>
 </span><span id="L-11"><a href="#L-11"><span class="linenos"> 11</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-12"><a href="#L-12"><span class="linenos"> 12</span></a><span class="sd">    | --- | --- |</span>
@@ -175,7 +175,7 @@
 </span><span id="L-28"><a href="#L-28"><span class="linenos"> 28</span></a><span class="k">def</span> <span class="nf">arithmetic_progression_term</span><span class="p">(</span><span class="n">max_d</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
 </span><span id="L-29"><a href="#L-29"><span class="linenos"> 29</span></a>                                <span class="n">max_a</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
 </span><span id="L-30"><a href="#L-30"><span class="linenos"> 30</span></a>                                <span class="n">max_n</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="L-31"><a href="#L-31"><span class="linenos"> 31</span></a>    <span class="sd">&quot;&quot;&quot;Arithmetic Progression Term</span>
+</span><span id="L-31"><a href="#L-31"><span class="linenos"> 31</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Arithmetic Progression Term</span>
 </span><span id="L-32"><a href="#L-32"><span class="linenos"> 32</span></a>
 </span><span id="L-33"><a href="#L-33"><span class="linenos"> 33</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-34"><a href="#L-34"><span class="linenos"> 34</span></a><span class="sd">    | --- | --- |</span>
@@ -194,7 +194,7 @@
 </span><span id="L-47"><a href="#L-47"><span class="linenos"> 47</span></a>
 </span><span id="L-48"><a href="#L-48"><span class="linenos"> 48</span></a>
 </span><span id="L-49"><a href="#L-49"><span class="linenos"> 49</span></a><span class="k">def</span> <span class="nf">_fromBaseTenTo</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">to_base</span><span class="p">):</span>
-</span><span id="L-50"><a href="#L-50"><span class="linenos"> 50</span></a>    <span class="sd">&quot;&quot;&quot;Converts a decimal number n to another base, to_base.</span>
+</span><span id="L-50"><a href="#L-50"><span class="linenos"> 50</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Converts a decimal number n to another base, to_base.</span>
 </span><span id="L-51"><a href="#L-51"><span class="linenos"> 51</span></a><span class="sd">    Utility of base_conversion()</span>
 </span><span id="L-52"><a href="#L-52"><span class="linenos"> 52</span></a><span class="sd">    &quot;&quot;&quot;</span>
 </span><span id="L-53"><a href="#L-53"><span class="linenos"> 53</span></a>    <span class="n">alpha</span> <span class="o">=</span> <span class="s2">&quot;0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ&quot;</span>
@@ -219,7 +219,7 @@
 </span><span id="L-72"><a href="#L-72"><span class="linenos"> 72</span></a>
 </span><span id="L-73"><a href="#L-73"><span class="linenos"> 73</span></a>
 </span><span id="L-74"><a href="#L-74"><span class="linenos"> 74</span></a><span class="k">def</span> <span class="nf">base_conversion</span><span class="p">(</span><span class="n">max_num</span><span class="o">=</span><span class="mi">60000</span><span class="p">,</span> <span class="n">max_base</span><span class="o">=</span><span class="mi">16</span><span class="p">):</span>
-</span><span id="L-75"><a href="#L-75"><span class="linenos"> 75</span></a>    <span class="sd">&quot;&quot;&quot;Base Conversion</span>
+</span><span id="L-75"><a href="#L-75"><span class="linenos"> 75</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Base Conversion</span>
 </span><span id="L-76"><a href="#L-76"><span class="linenos"> 76</span></a>
 </span><span id="L-77"><a href="#L-77"><span class="linenos"> 77</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-78"><a href="#L-78"><span class="linenos"> 78</span></a><span class="sd">    | --- | --- |</span>
@@ -241,18 +241,18 @@
 </span><span id="L-94"><a href="#L-94"><span class="linenos"> 94</span></a>    <span class="k">while</span> <span class="n">bases</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">==</span> <span class="n">bases</span><span class="p">[</span><span class="mi">1</span><span class="p">]:</span>
 </span><span id="L-95"><a href="#L-95"><span class="linenos"> 95</span></a>        <span class="n">bases</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">choices</span><span class="p">(</span><span class="n">dist</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
 </span><span id="L-96"><a href="#L-96"><span class="linenos"> 96</span></a>
-</span><span id="L-97"><a href="#L-97"><span class="linenos"> 97</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Convert $</span><span class="si">{</span><span class="n">_fromBaseTenTo</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">bases</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="si">}</span><span class="s2">$ from base $</span><span class="si">{</span><span class="n">bases</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="si">}</span><span class="s2">$ to base $</span><span class="si">{</span><span class="n">bases</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="si">}</span><span class="s2">$.&quot;</span>
+</span><span id="L-97"><a href="#L-97"><span class="linenos"> 97</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Convert $</span><span class="si">{</span><span class="n">_fromBaseTenTo</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">bases</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="si">}</span><span class="s2">$ from base $</span><span class="si">{</span><span class="n">bases</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="si">}</span><span class="s2">$ to base $</span><span class="si">{</span><span class="n">bases</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="si">}</span><span class="s2">$.&quot;</span>
 </span><span id="L-98"><a href="#L-98"><span class="linenos"> 98</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="n">_fromBaseTenTo</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">bases</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
 </span><span id="L-99"><a href="#L-99"><span class="linenos"> 99</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s1">$&#39;</span>
 </span><span id="L-100"><a href="#L-100"><span class="linenos">100</span></a>
 </span><span id="L-101"><a href="#L-101"><span class="linenos">101</span></a>
 </span><span id="L-102"><a href="#L-102"><span class="linenos">102</span></a><span class="k">def</span> <span class="nf">_newton_symbol</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">k</span><span class="p">):</span>
-</span><span id="L-103"><a href="#L-103"><span class="linenos">103</span></a>    <span class="sd">&quot;&quot;&quot;Utility of binomial_distribution()&quot;&quot;&quot;</span>
+</span><span id="L-103"><a href="#L-103"><span class="linenos">103</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Utility of binomial_distribution()&quot;&quot;&quot;</span>
 </span><span id="L-104"><a href="#L-104"><span class="linenos">104</span></a>    <span class="k">return</span> <span class="n">math</span><span class="o">.</span><span class="n">factorial</span><span class="p">(</span><span class="n">n</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">factorial</span><span class="p">(</span><span class="n">k</span><span class="p">)</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">factorial</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="n">k</span><span class="p">))</span>
 </span><span id="L-105"><a href="#L-105"><span class="linenos">105</span></a>
 </span><span id="L-106"><a href="#L-106"><span class="linenos">106</span></a>
 </span><span id="L-107"><a href="#L-107"><span class="linenos">107</span></a><span class="k">def</span> <span class="nf">binomial_distribution</span><span class="p">():</span>
-</span><span id="L-108"><a href="#L-108"><span class="linenos">108</span></a>    <span class="sd">&quot;&quot;&quot;Binomial distribution</span>
+</span><span id="L-108"><a href="#L-108"><span class="linenos">108</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Binomial distribution</span>
 </span><span id="L-109"><a href="#L-109"><span class="linenos">109</span></a>
 </span><span id="L-110"><a href="#L-110"><span class="linenos">110</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-111"><a href="#L-111"><span class="linenos">111</span></a><span class="sd">    | --- | --- |</span>
@@ -279,7 +279,7 @@
 </span><span id="L-132"><a href="#L-132"><span class="linenos">132</span></a>
 </span><span id="L-133"><a href="#L-133"><span class="linenos">133</span></a>
 </span><span id="L-134"><a href="#L-134"><span class="linenos">134</span></a><span class="k">def</span> <span class="nf">celsius_to_fahrenheit</span><span class="p">(</span><span class="n">max_temp</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="L-135"><a href="#L-135"><span class="linenos">135</span></a>    <span class="sd">&quot;&quot;&quot;Celsius to Fahrenheit</span>
+</span><span id="L-135"><a href="#L-135"><span class="linenos">135</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Celsius to Fahrenheit</span>
 </span><span id="L-136"><a href="#L-136"><span class="linenos">136</span></a>
 </span><span id="L-137"><a href="#L-137"><span class="linenos">137</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-138"><a href="#L-138"><span class="linenos">138</span></a><span class="sd">    | --- | --- |</span>
@@ -294,7 +294,7 @@
 </span><span id="L-147"><a href="#L-147"><span class="linenos">147</span></a>
 </span><span id="L-148"><a href="#L-148"><span class="linenos">148</span></a>
 </span><span id="L-149"><a href="#L-149"><span class="linenos">149</span></a><span class="k">def</span> <span class="nf">common_factors</span><span class="p">(</span><span class="n">max_val</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="L-150"><a href="#L-150"><span class="linenos">150</span></a>    <span class="sd">&quot;&quot;&quot;Common Factors</span>
+</span><span id="L-150"><a href="#L-150"><span class="linenos">150</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Common Factors</span>
 </span><span id="L-151"><a href="#L-151"><span class="linenos">151</span></a>
 </span><span id="L-152"><a href="#L-152"><span class="linenos">152</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-153"><a href="#L-153"><span class="linenos">153</span></a><span class="sd">    | --- | --- |</span>
@@ -324,7 +324,7 @@
 </span><span id="L-177"><a href="#L-177"><span class="linenos">177</span></a>
 </span><span id="L-178"><a href="#L-178"><span class="linenos">178</span></a><span class="k">def</span> <span class="nf">complex_to_polar</span><span class="p">(</span><span class="n">min_real_imaginary_num</span><span class="o">=-</span><span class="mi">20</span><span class="p">,</span>
 </span><span id="L-179"><a href="#L-179"><span class="linenos">179</span></a>                     <span class="n">max_real_imaginary_num</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="L-180"><a href="#L-180"><span class="linenos">180</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Complex to polar form</span>
+</span><span id="L-180"><a href="#L-180"><span class="linenos">180</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Complex to polar form</span>
 </span><span id="L-181"><a href="#L-181"><span class="linenos">181</span></a>
 </span><span id="L-182"><a href="#L-182"><span class="linenos">182</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-183"><a href="#L-183"><span class="linenos">183</span></a><span class="sd">    | --- | --- |</span>
@@ -342,7 +342,7 @@
 </span><span id="L-195"><a href="#L-195"><span class="linenos">195</span></a>
 </span><span id="L-196"><a href="#L-196"><span class="linenos">196</span></a>
 </span><span id="L-197"><a href="#L-197"><span class="linenos">197</span></a><span class="k">def</span> <span class="nf">decimal_to_roman_numerals</span><span class="p">(</span><span class="n">max_decimal</span><span class="o">=</span><span class="mi">4000</span><span class="p">):</span>
-</span><span id="L-198"><a href="#L-198"><span class="linenos">198</span></a>    <span class="sd">&quot;&quot;&quot;Decimal to Roman Numerals</span>
+</span><span id="L-198"><a href="#L-198"><span class="linenos">198</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Decimal to Roman Numerals</span>
 </span><span id="L-199"><a href="#L-199"><span class="linenos">199</span></a>
 </span><span id="L-200"><a href="#L-200"><span class="linenos">200</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-201"><a href="#L-201"><span class="linenos">201</span></a><span class="sd">    | --- | --- |</span>
@@ -382,7 +382,7 @@
 </span><span id="L-235"><a href="#L-235"><span class="linenos">235</span></a>
 </span><span id="L-236"><a href="#L-236"><span class="linenos">236</span></a>
 </span><span id="L-237"><a href="#L-237"><span class="linenos">237</span></a><span class="k">def</span> <span class="nf">euclidian_norm</span><span class="p">(</span><span class="n">maxEltAmt</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="L-238"><a href="#L-238"><span class="linenos">238</span></a>    <span class="sd">&quot;&quot;&quot;Euclidian norm or L2 norm of a vector</span>
+</span><span id="L-238"><a href="#L-238"><span class="linenos">238</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Euclidian norm or L2 norm of a vector</span>
 </span><span id="L-239"><a href="#L-239"><span class="linenos">239</span></a>
 </span><span id="L-240"><a href="#L-240"><span class="linenos">240</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-241"><a href="#L-241"><span class="linenos">241</span></a><span class="sd">    | --- | --- |</span>
@@ -398,7 +398,7 @@
 </span><span id="L-251"><a href="#L-251"><span class="linenos">251</span></a>
 </span><span id="L-252"><a href="#L-252"><span class="linenos">252</span></a>
 </span><span id="L-253"><a href="#L-253"><span class="linenos">253</span></a><span class="k">def</span> <span class="nf">factors</span><span class="p">(</span><span class="n">max_val</span><span class="o">=</span><span class="mi">1000</span><span class="p">):</span>
-</span><span id="L-254"><a href="#L-254"><span class="linenos">254</span></a>    <span class="sd">&quot;&quot;&quot;Factors of a number</span>
+</span><span id="L-254"><a href="#L-254"><span class="linenos">254</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Factors of a number</span>
 </span><span id="L-255"><a href="#L-255"><span class="linenos">255</span></a>
 </span><span id="L-256"><a href="#L-256"><span class="linenos">256</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-257"><a href="#L-257"><span class="linenos">257</span></a><span class="sd">    | --- | --- |</span>
@@ -425,7 +425,7 @@
 </span><span id="L-278"><a href="#L-278"><span class="linenos">278</span></a>
 </span><span id="L-279"><a href="#L-279"><span class="linenos">279</span></a>
 </span><span id="L-280"><a href="#L-280"><span class="linenos">280</span></a><span class="k">def</span> <span class="nf">geometric_mean</span><span class="p">(</span><span class="n">max_value</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">max_count</span><span class="o">=</span><span class="mi">4</span><span class="p">):</span>
-</span><span id="L-281"><a href="#L-281"><span class="linenos">281</span></a>    <span class="sd">&quot;&quot;&quot;Geometric Mean of N Numbers</span>
+</span><span id="L-281"><a href="#L-281"><span class="linenos">281</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Geometric Mean of N Numbers</span>
 </span><span id="L-282"><a href="#L-282"><span class="linenos">282</span></a>
 </span><span id="L-283"><a href="#L-283"><span class="linenos">283</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-284"><a href="#L-284"><span class="linenos">284</span></a><span class="sd">    | --- | --- |</span>
@@ -447,7 +447,7 @@
 </span><span id="L-300"><a href="#L-300"><span class="linenos">300</span></a>                          <span class="n">max_value</span><span class="o">=</span><span class="mi">12</span><span class="p">,</span>
 </span><span id="L-301"><a href="#L-301"><span class="linenos">301</span></a>                          <span class="n">n_term</span><span class="o">=</span><span class="mi">7</span><span class="p">,</span>
 </span><span id="L-302"><a href="#L-302"><span class="linenos">302</span></a>                          <span class="n">sum_term</span><span class="o">=</span><span class="mi">5</span><span class="p">):</span>
-</span><span id="L-303"><a href="#L-303"><span class="linenos">303</span></a>    <span class="sd">&quot;&quot;&quot;Geometric Progression</span>
+</span><span id="L-303"><a href="#L-303"><span class="linenos">303</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Geometric Progression</span>
 </span><span id="L-304"><a href="#L-304"><span class="linenos">304</span></a>
 </span><span id="L-305"><a href="#L-305"><span class="linenos">305</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-306"><a href="#L-306"><span class="linenos">306</span></a><span class="sd">    | --- | --- |</span>
@@ -470,7 +470,7 @@
 </span><span id="L-323"><a href="#L-323"><span class="linenos">323</span></a>
 </span><span id="L-324"><a href="#L-324"><span class="linenos">324</span></a>
 </span><span id="L-325"><a href="#L-325"><span class="linenos">325</span></a><span class="k">def</span> <span class="nf">harmonic_mean</span><span class="p">(</span><span class="n">max_value</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">max_count</span><span class="o">=</span><span class="mi">4</span><span class="p">):</span>
-</span><span id="L-326"><a href="#L-326"><span class="linenos">326</span></a>    <span class="sd">&quot;&quot;&quot;Harmonic Mean of N Numbers</span>
+</span><span id="L-326"><a href="#L-326"><span class="linenos">326</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Harmonic Mean of N Numbers</span>
 </span><span id="L-327"><a href="#L-327"><span class="linenos">327</span></a>
 </span><span id="L-328"><a href="#L-328"><span class="linenos">328</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-329"><a href="#L-329"><span class="linenos">329</span></a><span class="sd">    | --- | --- |</span>
@@ -483,13 +483,13 @@
 </span><span id="L-336"><a href="#L-336"><span class="linenos">336</span></a>        <span class="nb">sum</span> <span class="o">+=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">num</span><span class="p">)</span>
 </span><span id="L-337"><a href="#L-337"><span class="linenos">337</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">num</span> <span class="o">/</span> <span class="nb">sum</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
 </span><span id="L-338"><a href="#L-338"><span class="linenos">338</span></a>
-</span><span id="L-339"><a href="#L-339"><span class="linenos">339</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Harmonic mean of $</span><span class="si">{</span><span class="n">count</span><span class="si">}</span><span class="s2">$ numbers $</span><span class="si">{</span><span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="n">nums</span><span class="p">))</span><span class="si">}</span><span class="s2"> = $&quot;</span>
+</span><span id="L-339"><a href="#L-339"><span class="linenos">339</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Harmonic mean of $</span><span class="si">{</span><span class="n">count</span><span class="si">}</span><span class="s2">$ numbers $</span><span class="si">{</span><span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">))</span><span class="si">}</span><span class="s2"> = $&quot;</span>
 </span><span id="L-340"><a href="#L-340"><span class="linenos">340</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2">$&quot;</span>
 </span><span id="L-341"><a href="#L-341"><span class="linenos">341</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span><span id="L-342"><a href="#L-342"><span class="linenos">342</span></a>
 </span><span id="L-343"><a href="#L-343"><span class="linenos">343</span></a>
 </span><span id="L-344"><a href="#L-344"><span class="linenos">344</span></a><span class="k">def</span> <span class="nf">is_leap_year</span><span class="p">(</span><span class="n">minNumber</span><span class="o">=</span><span class="mi">1900</span><span class="p">,</span> <span class="n">max_number</span><span class="o">=</span><span class="mi">2099</span><span class="p">):</span>
-</span><span id="L-345"><a href="#L-345"><span class="linenos">345</span></a>    <span class="sd">&quot;&quot;&quot;Is Leap Year or Not</span>
+</span><span id="L-345"><a href="#L-345"><span class="linenos">345</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Is Leap Year or Not</span>
 </span><span id="L-346"><a href="#L-346"><span class="linenos">346</span></a>
 </span><span id="L-347"><a href="#L-347"><span class="linenos">347</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-348"><a href="#L-348"><span class="linenos">348</span></a><span class="sd">    | --- | --- |</span>
@@ -508,12 +508,12 @@
 </span><span id="L-361"><a href="#L-361"><span class="linenos">361</span></a>    <span class="k">else</span><span class="p">:</span>
 </span><span id="L-362"><a href="#L-362"><span class="linenos">362</span></a>        <span class="n">ans</span> <span class="o">=</span> <span class="kc">False</span>
 </span><span id="L-363"><a href="#L-363"><span class="linenos">363</span></a>
-</span><span id="L-364"><a href="#L-364"><span class="linenos">364</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">year</span><span class="si">}</span><span class="s2"> is</span><span class="si">{</span><span class="s1">&#39; not&#39;</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">ans</span> <span class="k">else</span> <span class="s1">&#39;&#39;</span><span class="si">}</span><span class="s2"> a leap year&quot;</span>
+</span><span id="L-364"><a href="#L-364"><span class="linenos">364</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">year</span><span class="si">}</span><span class="s2"> is</span><span class="si">{</span><span class="s1">&#39; not&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="ow">not</span><span class="w"> </span><span class="n">ans</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="s1">&#39;&#39;</span><span class="si">}</span><span class="s2"> a leap year&quot;</span>
 </span><span id="L-365"><a href="#L-365"><span class="linenos">365</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span><span id="L-366"><a href="#L-366"><span class="linenos">366</span></a>
 </span><span id="L-367"><a href="#L-367"><span class="linenos">367</span></a>
 </span><span id="L-368"><a href="#L-368"><span class="linenos">368</span></a><span class="k">def</span> <span class="nf">lcm</span><span class="p">(</span><span class="n">max_val</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="L-369"><a href="#L-369"><span class="linenos">369</span></a>    <span class="sd">&quot;&quot;&quot;LCM (Least Common Multiple)</span>
+</span><span id="L-369"><a href="#L-369"><span class="linenos">369</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;LCM (Least Common Multiple)</span>
 </span><span id="L-370"><a href="#L-370"><span class="linenos">370</span></a>
 </span><span id="L-371"><a href="#L-371"><span class="linenos">371</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-372"><a href="#L-372"><span class="linenos">372</span></a><span class="sd">    | --- | --- |</span>
@@ -534,7 +534,7 @@
 </span><span id="L-387"><a href="#L-387"><span class="linenos">387</span></a>
 </span><span id="L-388"><a href="#L-388"><span class="linenos">388</span></a>
 </span><span id="L-389"><a href="#L-389"><span class="linenos">389</span></a><span class="k">def</span> <span class="nf">minutes_to_hours</span><span class="p">(</span><span class="n">max_minutes</span><span class="o">=</span><span class="mi">999</span><span class="p">):</span>
-</span><span id="L-390"><a href="#L-390"><span class="linenos">390</span></a>    <span class="sd">&quot;&quot;&quot;Convert minutes to hours and minutes</span>
+</span><span id="L-390"><a href="#L-390"><span class="linenos">390</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Convert minutes to hours and minutes</span>
 </span><span id="L-391"><a href="#L-391"><span class="linenos">391</span></a>
 </span><span id="L-392"><a href="#L-392"><span class="linenos">392</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-393"><a href="#L-393"><span class="linenos">393</span></a><span class="sd">    | --- | --- |</span>
@@ -550,7 +550,7 @@
 </span><span id="L-403"><a href="#L-403"><span class="linenos">403</span></a>
 </span><span id="L-404"><a href="#L-404"><span class="linenos">404</span></a>
 </span><span id="L-405"><a href="#L-405"><span class="linenos">405</span></a><span class="k">def</span> <span class="nf">prime_factors</span><span class="p">(</span><span class="n">min_val</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_val</span><span class="o">=</span><span class="mi">200</span><span class="p">):</span>
-</span><span id="L-406"><a href="#L-406"><span class="linenos">406</span></a>    <span class="sd">&quot;&quot;&quot;Prime Factors</span>
+</span><span id="L-406"><a href="#L-406"><span class="linenos">406</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Prime Factors</span>
 </span><span id="L-407"><a href="#L-407"><span class="linenos">407</span></a>
 </span><span id="L-408"><a href="#L-408"><span class="linenos">408</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-409"><a href="#L-409"><span class="linenos">409</span></a><span class="sd">    | --- | --- |</span>
@@ -572,12 +572,12 @@
 </span><span id="L-425"><a href="#L-425"><span class="linenos">425</span></a>        <span class="n">factors</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
 </span><span id="L-426"><a href="#L-426"><span class="linenos">426</span></a>
 </span><span id="L-427"><a href="#L-427"><span class="linenos">427</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Find prime factors of $</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="s2">$&quot;</span>
-</span><span id="L-428"><a href="#L-428"><span class="linenos">428</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="n">factors</span><span class="p">))</span><span class="si">}</span><span class="s2">$&quot;</span>
+</span><span id="L-428"><a href="#L-428"><span class="linenos">428</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span><span class="w"> </span><span class="n">factors</span><span class="p">))</span><span class="si">}</span><span class="s2">$&quot;</span>
 </span><span id="L-429"><a href="#L-429"><span class="linenos">429</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span><span id="L-430"><a href="#L-430"><span class="linenos">430</span></a>
 </span><span id="L-431"><a href="#L-431"><span class="linenos">431</span></a>
 </span><span id="L-432"><a href="#L-432"><span class="linenos">432</span></a><span class="k">def</span> <span class="nf">product_of_scientific_notations</span><span class="p">(</span><span class="n">min_exp_val</span><span class="o">=-</span><span class="mi">100</span><span class="p">,</span> <span class="n">max_exp_val</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="L-433"><a href="#L-433"><span class="linenos">433</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Product of scientific notations</span>
+</span><span id="L-433"><a href="#L-433"><span class="linenos">433</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Product of scientific notations</span>
 </span><span id="L-434"><a href="#L-434"><span class="linenos">434</span></a>
 </span><span id="L-435"><a href="#L-435"><span class="linenos">435</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-436"><a href="#L-436"><span class="linenos">436</span></a><span class="sd">    | --- | --- |</span>
@@ -594,12 +594,12 @@
 </span><span id="L-447"><a href="#L-447"><span class="linenos">447</span></a>        <span class="n">c</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
 </span><span id="L-448"><a href="#L-448"><span class="linenos">448</span></a>
 </span><span id="L-449"><a href="#L-449"><span class="linenos">449</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">rf</span><span class="s2">&quot;Product of scientific notations $</span><span class="si">{</span><span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="si">}</span><span class="s2"> \times 10^</span><span class="se">{{</span><span class="si">{</span><span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="si">}</span><span class="se">}}</span><span class="s2">$ and $</span><span class="si">{</span><span class="n">b</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="si">}</span><span class="s2"> \times 10^</span><span class="se">{{</span><span class="si">{</span><span class="n">b</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="si">}</span><span class="se">}}</span><span class="s2"> = $&quot;</span>
-</span><span id="L-450"><a href="#L-450"><span class="linenos">450</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;$</span><span class="si">{</span><span class="nb">round</span><span class="p">(</span><span class="n">c</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="mi">2</span><span class="p">)</span><span class="si">}</span><span class="s1"> \times 10^</span><span class="se">{{</span><span class="si">{</span><span class="n">c</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="si">}</span><span class="se">}}</span><span class="s1">$&#39;</span>
+</span><span id="L-450"><a href="#L-450"><span class="linenos">450</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;$</span><span class="si">{</span><span class="nb">round</span><span class="p">(</span><span class="n">c</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="si">}</span><span class="s1"> \times 10^</span><span class="se">{{</span><span class="si">{</span><span class="n">c</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="si">}</span><span class="se">}}</span><span class="s1">$&#39;</span>
 </span><span id="L-451"><a href="#L-451"><span class="linenos">451</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span><span id="L-452"><a href="#L-452"><span class="linenos">452</span></a>
 </span><span id="L-453"><a href="#L-453"><span class="linenos">453</span></a>
 </span><span id="L-454"><a href="#L-454"><span class="linenos">454</span></a><span class="k">def</span> <span class="nf">profit_loss_percent</span><span class="p">(</span><span class="n">max_cp</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span> <span class="n">max_sp</span><span class="o">=</span><span class="mi">1000</span><span class="p">):</span>
-</span><span id="L-455"><a href="#L-455"><span class="linenos">455</span></a>    <span class="sd">&quot;&quot;&quot;Profit or Loss Percent</span>
+</span><span id="L-455"><a href="#L-455"><span class="linenos">455</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Profit or Loss Percent</span>
 </span><span id="L-456"><a href="#L-456"><span class="linenos">456</span></a>
 </span><span id="L-457"><a href="#L-457"><span class="linenos">457</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-458"><a href="#L-458"><span class="linenos">458</span></a><span class="sd">    | --- | --- |</span>
@@ -619,11 +619,11 @@
 </span><span id="L-472"><a href="#L-472"><span class="linenos">472</span></a>
 </span><span id="L-473"><a href="#L-473"><span class="linenos">473</span></a>
 </span><span id="L-474"><a href="#L-474"><span class="linenos">474</span></a><span class="k">def</span> <span class="nf">quotient_of_power_same_base</span><span class="p">(</span><span class="n">max_base</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">max_power</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-475"><a href="#L-475"><span class="linenos">475</span></a>    <span class="sd">&quot;&quot;&quot;Quotient of Powers with Same Base</span>
+</span><span id="L-475"><a href="#L-475"><span class="linenos">475</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Quotient of Powers with Same Base</span>
 </span><span id="L-476"><a href="#L-476"><span class="linenos">476</span></a>
 </span><span id="L-477"><a href="#L-477"><span class="linenos">477</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-478"><a href="#L-478"><span class="linenos">478</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="L-479"><a href="#L-479"><span class="linenos">479</span></a><span class="sd">    | The Quotient of $5^{6}$ and $5^{8} = $5^{6-8} = 5^{-2}$ | $0.04$ |</span>
+</span><span id="L-479"><a href="#L-479"><span class="linenos">479</span></a><span class="sd">    | The Quotient of $5^{6}$ and $5^{8} = 5^{6-8} = 5^{-2}$ | $0.04$ |</span>
 </span><span id="L-480"><a href="#L-480"><span class="linenos">480</span></a><span class="sd">    &quot;&quot;&quot;</span>
 </span><span id="L-481"><a href="#L-481"><span class="linenos">481</span></a>    <span class="n">base</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_base</span><span class="p">)</span>
 </span><span id="L-482"><a href="#L-482"><span class="linenos">482</span></a>    <span class="n">power1</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_power</span><span class="p">)</span>
@@ -632,12 +632,12 @@
 </span><span id="L-485"><a href="#L-485"><span class="linenos">485</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="n">base</span> <span class="o">**</span> <span class="n">step</span>
 </span><span id="L-486"><a href="#L-486"><span class="linenos">486</span></a>
 </span><span id="L-487"><a href="#L-487"><span class="linenos">487</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;The Quotient of $</span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2">^</span><span class="se">{{</span><span class="si">{</span><span class="n">power1</span><span class="si">}</span><span class="se">}}</span><span class="s2">$ and $</span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2">^</span><span class="se">{{</span><span class="si">{</span><span class="n">power2</span><span class="si">}</span><span class="se">}}</span><span class="s2"> = &quot;</span> \
-</span><span id="L-488"><a href="#L-488"><span class="linenos">488</span></a>        <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2">^</span><span class="se">{{</span><span class="si">{</span><span class="n">power1</span><span class="si">}</span><span class="s2">-</span><span class="si">{</span><span class="n">power2</span><span class="si">}</span><span class="se">}}</span><span class="s2"> = </span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2">^</span><span class="se">{{</span><span class="si">{</span><span class="n">step</span><span class="si">}</span><span class="se">}}</span><span class="s2">$&quot;</span>
+</span><span id="L-488"><a href="#L-488"><span class="linenos">488</span></a>        <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2">^</span><span class="se">{{</span><span class="si">{</span><span class="n">power1</span><span class="si">}</span><span class="s2">-</span><span class="si">{</span><span class="n">power2</span><span class="si">}</span><span class="se">}}</span><span class="s2"> = </span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2">^</span><span class="se">{{</span><span class="si">{</span><span class="n">step</span><span class="si">}</span><span class="se">}}</span><span class="s2">$&quot;</span>
 </span><span id="L-489"><a href="#L-489"><span class="linenos">489</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="n">solution</span><span class="si">}</span><span class="s1">$&#39;</span>
 </span><span id="L-490"><a href="#L-490"><span class="linenos">490</span></a>
 </span><span id="L-491"><a href="#L-491"><span class="linenos">491</span></a>
 </span><span id="L-492"><a href="#L-492"><span class="linenos">492</span></a><span class="k">def</span> <span class="nf">quotient_of_power_same_power</span><span class="p">(</span><span class="n">max_base</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">max_power</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-493"><a href="#L-493"><span class="linenos">493</span></a>    <span class="sd">&quot;&quot;&quot;Quotient of Powers with Same Power</span>
+</span><span id="L-493"><a href="#L-493"><span class="linenos">493</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Quotient of Powers with Same Power</span>
 </span><span id="L-494"><a href="#L-494"><span class="linenos">494</span></a>
 </span><span id="L-495"><a href="#L-495"><span class="linenos">495</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-496"><a href="#L-496"><span class="linenos">496</span></a><span class="sd">    | --- | --- |</span>
@@ -655,11 +655,11 @@
 </span><span id="L-508"><a href="#L-508"><span class="linenos">508</span></a>
 </span><span id="L-509"><a href="#L-509"><span class="linenos">509</span></a>
 </span><span id="L-510"><a href="#L-510"><span class="linenos">510</span></a><span class="k">def</span> <span class="nf">set_operation</span><span class="p">(</span><span class="n">min_size</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">max_size</span><span class="o">=</span><span class="mi">7</span><span class="p">):</span>
-</span><span id="L-511"><a href="#L-511"><span class="linenos">511</span></a>    <span class="sd">&quot;&quot;&quot;Union, Intersection, Difference of Two Sets</span>
+</span><span id="L-511"><a href="#L-511"><span class="linenos">511</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Union, Intersection, Difference of Two Sets</span>
 </span><span id="L-512"><a href="#L-512"><span class="linenos">512</span></a>
 </span><span id="L-513"><a href="#L-513"><span class="linenos">513</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-514"><a href="#L-514"><span class="linenos">514</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="L-515"><a href="#L-515"><span class="linenos">515</span></a><span class="sd">    | Given the two sets $a={1, 2, 4, 5}$, $b={8, 1, 2}. Find the Union, intersection, a-b, b-a, and symmetric difference | Union is ${1, 2, 4, 5, 8}$. Intersection is ${1, 2}$, a-b is ${4, 5}$, b-a is ${8}$. Symmetric difference is ${4, 5, 8}$. |</span>
+</span><span id="L-515"><a href="#L-515"><span class="linenos">515</span></a><span class="sd">    | Given the two sets $a={1, 2, 4, 5}$, $b={8, 1, 2}$. Find the Union, intersection, $a-b$, $b-a$, and symmetric difference | Union is ${1, 2, 4, 5, 8}$. Intersection is ${1, 2}$, $a-b$ is ${4, 5}$, $b-a$ is ${8}$. Symmetric difference is ${4, 5, 8}$. |</span>
 </span><span id="L-516"><a href="#L-516"><span class="linenos">516</span></a><span class="sd">    &quot;&quot;&quot;</span>
 </span><span id="L-517"><a href="#L-517"><span class="linenos">517</span></a>    <span class="n">number_variables_a</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="n">min_size</span><span class="p">,</span> <span class="n">max_size</span><span class="p">)</span>
 </span><span id="L-518"><a href="#L-518"><span class="linenos">518</span></a>    <span class="n">number_variables_b</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="n">min_size</span><span class="p">,</span> <span class="n">max_size</span><span class="p">)</span>
@@ -672,16 +672,16 @@
 </span><span id="L-525"><a href="#L-525"><span class="linenos">525</span></a>    <span class="n">a</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
 </span><span id="L-526"><a href="#L-526"><span class="linenos">526</span></a>    <span class="n">b</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
 </span><span id="L-527"><a href="#L-527"><span class="linenos">527</span></a>
-</span><span id="L-528"><a href="#L-528"><span class="linenos">528</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Given the two sets $a=</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="s2">$, $b=</span><span class="si">{</span><span class="n">b</span><span class="si">}</span><span class="s2">. &quot;</span> <span class="o">+</span> \
-</span><span id="L-529"><a href="#L-529"><span class="linenos">529</span></a>        <span class="s2">&quot;Find the Union, intersection, a-b, b-a, and symmetric difference&quot;</span>
+</span><span id="L-528"><a href="#L-528"><span class="linenos">528</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Given the two sets $a=</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="s2">$, $b=</span><span class="si">{</span><span class="n">b</span><span class="si">}</span><span class="s2">$. &quot;</span> <span class="o">+</span> \
+</span><span id="L-529"><a href="#L-529"><span class="linenos">529</span></a>        <span class="s2">&quot;Find the Union, intersection, $a-b$, $b-a$, and symmetric difference&quot;</span>
 </span><span id="L-530"><a href="#L-530"><span class="linenos">530</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Union is $</span><span class="si">{</span><span class="n">a</span><span class="o">.</span><span class="n">union</span><span class="p">(</span><span class="n">b</span><span class="p">)</span><span class="si">}</span><span class="s2">$. Intersection is $</span><span class="si">{</span><span class="n">a</span><span class="o">.</span><span class="n">intersection</span><span class="p">(</span><span class="n">b</span><span class="p">)</span><span class="si">}</span><span class="s2">$&quot;</span> <span class="o">+</span> \
-</span><span id="L-531"><a href="#L-531"><span class="linenos">531</span></a>        <span class="sa">f</span><span class="s2">&quot;, a-b is $</span><span class="si">{</span><span class="n">a</span><span class="o">.</span><span class="n">difference</span><span class="p">(</span><span class="n">b</span><span class="p">)</span><span class="si">}</span><span class="s2">$, b-a is $</span><span class="si">{</span><span class="n">b</span><span class="o">.</span><span class="n">difference</span><span class="p">(</span><span class="n">a</span><span class="p">)</span><span class="si">}</span><span class="s2">$.&quot;</span> <span class="o">+</span> \
+</span><span id="L-531"><a href="#L-531"><span class="linenos">531</span></a>        <span class="sa">f</span><span class="s2">&quot;, $a-b$ is $</span><span class="si">{</span><span class="n">a</span><span class="o">.</span><span class="n">difference</span><span class="p">(</span><span class="n">b</span><span class="p">)</span><span class="si">}</span><span class="s2">$, $b-a$ is $</span><span class="si">{</span><span class="n">b</span><span class="o">.</span><span class="n">difference</span><span class="p">(</span><span class="n">a</span><span class="p">)</span><span class="si">}</span><span class="s2">$.&quot;</span> <span class="o">+</span> \
 </span><span id="L-532"><a href="#L-532"><span class="linenos">532</span></a>        <span class="sa">f</span><span class="s2">&quot; Symmetric difference is $</span><span class="si">{</span><span class="n">a</span><span class="o">.</span><span class="n">symmetric_difference</span><span class="p">(</span><span class="n">b</span><span class="p">)</span><span class="si">}</span><span class="s2">$.&quot;</span>
 </span><span id="L-533"><a href="#L-533"><span class="linenos">533</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span><span id="L-534"><a href="#L-534"><span class="linenos">534</span></a>
 </span><span id="L-535"><a href="#L-535"><span class="linenos">535</span></a>
 </span><span id="L-536"><a href="#L-536"><span class="linenos">536</span></a><span class="k">def</span> <span class="nf">signum_function</span><span class="p">(</span><span class="nb">min</span><span class="o">=-</span><span class="mi">999</span><span class="p">,</span> <span class="nb">max</span><span class="o">=</span><span class="mi">999</span><span class="p">):</span>
-</span><span id="L-537"><a href="#L-537"><span class="linenos">537</span></a>    <span class="sd">&quot;&quot;&quot;Signum Function</span>
+</span><span id="L-537"><a href="#L-537"><span class="linenos">537</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Signum Function</span>
 </span><span id="L-538"><a href="#L-538"><span class="linenos">538</span></a>
 </span><span id="L-539"><a href="#L-539"><span class="linenos">539</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-540"><a href="#L-540"><span class="linenos">540</span></a><span class="sd">    | --- | --- |</span>
@@ -700,7 +700,7 @@
 </span><span id="L-553"><a href="#L-553"><span class="linenos">553</span></a>
 </span><span id="L-554"><a href="#L-554"><span class="linenos">554</span></a>
 </span><span id="L-555"><a href="#L-555"><span class="linenos">555</span></a><span class="k">def</span> <span class="nf">surds_comparison</span><span class="p">(</span><span class="n">max_value</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">max_root</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-556"><a href="#L-556"><span class="linenos">556</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Comparing Surds</span>
+</span><span id="L-556"><a href="#L-556"><span class="linenos">556</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Comparing Surds</span>
 </span><span id="L-557"><a href="#L-557"><span class="linenos">557</span></a>
 </span><span id="L-558"><a href="#L-558"><span class="linenos">558</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-559"><a href="#L-559"><span class="linenos">559</span></a><span class="sd">    | --- | --- |</span>
@@ -737,7 +737,7 @@
             <div class="pdoc-code codehilite"><pre><span></span><span id="arithmetic_progression_sum-7"><a href="#arithmetic_progression_sum-7"><span class="linenos"> 7</span></a><span class="k">def</span> <span class="nf">arithmetic_progression_sum</span><span class="p">(</span><span class="n">max_d</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
 </span><span id="arithmetic_progression_sum-8"><a href="#arithmetic_progression_sum-8"><span class="linenos"> 8</span></a>                               <span class="n">max_a</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
 </span><span id="arithmetic_progression_sum-9"><a href="#arithmetic_progression_sum-9"><span class="linenos"> 9</span></a>                               <span class="n">max_n</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="arithmetic_progression_sum-10"><a href="#arithmetic_progression_sum-10"><span class="linenos">10</span></a>    <span class="sd">&quot;&quot;&quot;Arithmetic Progression Sum</span>
+</span><span id="arithmetic_progression_sum-10"><a href="#arithmetic_progression_sum-10"><span class="linenos">10</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Arithmetic Progression Sum</span>
 </span><span id="arithmetic_progression_sum-11"><a href="#arithmetic_progression_sum-11"><span class="linenos">11</span></a>
 </span><span id="arithmetic_progression_sum-12"><a href="#arithmetic_progression_sum-12"><span class="linenos">12</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="arithmetic_progression_sum-13"><a href="#arithmetic_progression_sum-13"><span class="linenos">13</span></a><span class="sd">    | --- | --- |</span>
@@ -791,7 +791,7 @@
             <div class="pdoc-code codehilite"><pre><span></span><span id="arithmetic_progression_term-29"><a href="#arithmetic_progression_term-29"><span class="linenos">29</span></a><span class="k">def</span> <span class="nf">arithmetic_progression_term</span><span class="p">(</span><span class="n">max_d</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
 </span><span id="arithmetic_progression_term-30"><a href="#arithmetic_progression_term-30"><span class="linenos">30</span></a>                                <span class="n">max_a</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
 </span><span id="arithmetic_progression_term-31"><a href="#arithmetic_progression_term-31"><span class="linenos">31</span></a>                                <span class="n">max_n</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="arithmetic_progression_term-32"><a href="#arithmetic_progression_term-32"><span class="linenos">32</span></a>    <span class="sd">&quot;&quot;&quot;Arithmetic Progression Term</span>
+</span><span id="arithmetic_progression_term-32"><a href="#arithmetic_progression_term-32"><span class="linenos">32</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Arithmetic Progression Term</span>
 </span><span id="arithmetic_progression_term-33"><a href="#arithmetic_progression_term-33"><span class="linenos">33</span></a>
 </span><span id="arithmetic_progression_term-34"><a href="#arithmetic_progression_term-34"><span class="linenos">34</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="arithmetic_progression_term-35"><a href="#arithmetic_progression_term-35"><span class="linenos">35</span></a><span class="sd">    | --- | --- |</span>
@@ -842,7 +842,7 @@
     </div>
     <a class="headerlink" href="#base_conversion"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="base_conversion-75"><a href="#base_conversion-75"><span class="linenos"> 75</span></a><span class="k">def</span> <span class="nf">base_conversion</span><span class="p">(</span><span class="n">max_num</span><span class="o">=</span><span class="mi">60000</span><span class="p">,</span> <span class="n">max_base</span><span class="o">=</span><span class="mi">16</span><span class="p">):</span>
-</span><span id="base_conversion-76"><a href="#base_conversion-76"><span class="linenos"> 76</span></a>    <span class="sd">&quot;&quot;&quot;Base Conversion</span>
+</span><span id="base_conversion-76"><a href="#base_conversion-76"><span class="linenos"> 76</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Base Conversion</span>
 </span><span id="base_conversion-77"><a href="#base_conversion-77"><span class="linenos"> 77</span></a>
 </span><span id="base_conversion-78"><a href="#base_conversion-78"><span class="linenos"> 78</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="base_conversion-79"><a href="#base_conversion-79"><span class="linenos"> 79</span></a><span class="sd">    | --- | --- |</span>
@@ -864,7 +864,7 @@
 </span><span id="base_conversion-95"><a href="#base_conversion-95"><span class="linenos"> 95</span></a>    <span class="k">while</span> <span class="n">bases</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">==</span> <span class="n">bases</span><span class="p">[</span><span class="mi">1</span><span class="p">]:</span>
 </span><span id="base_conversion-96"><a href="#base_conversion-96"><span class="linenos"> 96</span></a>        <span class="n">bases</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">choices</span><span class="p">(</span><span class="n">dist</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
 </span><span id="base_conversion-97"><a href="#base_conversion-97"><span class="linenos"> 97</span></a>
-</span><span id="base_conversion-98"><a href="#base_conversion-98"><span class="linenos"> 98</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Convert $</span><span class="si">{</span><span class="n">_fromBaseTenTo</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">bases</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="si">}</span><span class="s2">$ from base $</span><span class="si">{</span><span class="n">bases</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="si">}</span><span class="s2">$ to base $</span><span class="si">{</span><span class="n">bases</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="si">}</span><span class="s2">$.&quot;</span>
+</span><span id="base_conversion-98"><a href="#base_conversion-98"><span class="linenos"> 98</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Convert $</span><span class="si">{</span><span class="n">_fromBaseTenTo</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">bases</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="si">}</span><span class="s2">$ from base $</span><span class="si">{</span><span class="n">bases</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="si">}</span><span class="s2">$ to base $</span><span class="si">{</span><span class="n">bases</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="si">}</span><span class="s2">$.&quot;</span>
 </span><span id="base_conversion-99"><a href="#base_conversion-99"><span class="linenos"> 99</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="n">_fromBaseTenTo</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">bases</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
 </span><span id="base_conversion-100"><a href="#base_conversion-100"><span class="linenos">100</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s1">$&#39;</span>
 </span></pre></div>
@@ -902,7 +902,7 @@
     </div>
     <a class="headerlink" href="#binomial_distribution"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="binomial_distribution-108"><a href="#binomial_distribution-108"><span class="linenos">108</span></a><span class="k">def</span> <span class="nf">binomial_distribution</span><span class="p">():</span>
-</span><span id="binomial_distribution-109"><a href="#binomial_distribution-109"><span class="linenos">109</span></a>    <span class="sd">&quot;&quot;&quot;Binomial distribution</span>
+</span><span id="binomial_distribution-109"><a href="#binomial_distribution-109"><span class="linenos">109</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Binomial distribution</span>
 </span><span id="binomial_distribution-110"><a href="#binomial_distribution-110"><span class="linenos">110</span></a>
 </span><span id="binomial_distribution-111"><a href="#binomial_distribution-111"><span class="linenos">111</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="binomial_distribution-112"><a href="#binomial_distribution-112"><span class="linenos">112</span></a><span class="sd">    | --- | --- |</span>
@@ -961,7 +961,7 @@
     </div>
     <a class="headerlink" href="#celsius_to_fahrenheit"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="celsius_to_fahrenheit-135"><a href="#celsius_to_fahrenheit-135"><span class="linenos">135</span></a><span class="k">def</span> <span class="nf">celsius_to_fahrenheit</span><span class="p">(</span><span class="n">max_temp</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="celsius_to_fahrenheit-136"><a href="#celsius_to_fahrenheit-136"><span class="linenos">136</span></a>    <span class="sd">&quot;&quot;&quot;Celsius to Fahrenheit</span>
+</span><span id="celsius_to_fahrenheit-136"><a href="#celsius_to_fahrenheit-136"><span class="linenos">136</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Celsius to Fahrenheit</span>
 </span><span id="celsius_to_fahrenheit-137"><a href="#celsius_to_fahrenheit-137"><span class="linenos">137</span></a>
 </span><span id="celsius_to_fahrenheit-138"><a href="#celsius_to_fahrenheit-138"><span class="linenos">138</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="celsius_to_fahrenheit-139"><a href="#celsius_to_fahrenheit-139"><span class="linenos">139</span></a><span class="sd">    | --- | --- |</span>
@@ -1008,7 +1008,7 @@
     </div>
     <a class="headerlink" href="#common_factors"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="common_factors-150"><a href="#common_factors-150"><span class="linenos">150</span></a><span class="k">def</span> <span class="nf">common_factors</span><span class="p">(</span><span class="n">max_val</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="common_factors-151"><a href="#common_factors-151"><span class="linenos">151</span></a>    <span class="sd">&quot;&quot;&quot;Common Factors</span>
+</span><span id="common_factors-151"><a href="#common_factors-151"><span class="linenos">151</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Common Factors</span>
 </span><span id="common_factors-152"><a href="#common_factors-152"><span class="linenos">152</span></a>
 </span><span id="common_factors-153"><a href="#common_factors-153"><span class="linenos">153</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="common_factors-154"><a href="#common_factors-154"><span class="linenos">154</span></a><span class="sd">    | --- | --- |</span>
@@ -1070,7 +1070,7 @@
     <a class="headerlink" href="#complex_to_polar"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="complex_to_polar-179"><a href="#complex_to_polar-179"><span class="linenos">179</span></a><span class="k">def</span> <span class="nf">complex_to_polar</span><span class="p">(</span><span class="n">min_real_imaginary_num</span><span class="o">=-</span><span class="mi">20</span><span class="p">,</span>
 </span><span id="complex_to_polar-180"><a href="#complex_to_polar-180"><span class="linenos">180</span></a>                     <span class="n">max_real_imaginary_num</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="complex_to_polar-181"><a href="#complex_to_polar-181"><span class="linenos">181</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Complex to polar form</span>
+</span><span id="complex_to_polar-181"><a href="#complex_to_polar-181"><span class="linenos">181</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Complex to polar form</span>
 </span><span id="complex_to_polar-182"><a href="#complex_to_polar-182"><span class="linenos">182</span></a>
 </span><span id="complex_to_polar-183"><a href="#complex_to_polar-183"><span class="linenos">183</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="complex_to_polar-184"><a href="#complex_to_polar-184"><span class="linenos">184</span></a><span class="sd">    | --- | --- |</span>
@@ -1120,7 +1120,7 @@
     </div>
     <a class="headerlink" href="#decimal_to_roman_numerals"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="decimal_to_roman_numerals-198"><a href="#decimal_to_roman_numerals-198"><span class="linenos">198</span></a><span class="k">def</span> <span class="nf">decimal_to_roman_numerals</span><span class="p">(</span><span class="n">max_decimal</span><span class="o">=</span><span class="mi">4000</span><span class="p">):</span>
-</span><span id="decimal_to_roman_numerals-199"><a href="#decimal_to_roman_numerals-199"><span class="linenos">199</span></a>    <span class="sd">&quot;&quot;&quot;Decimal to Roman Numerals</span>
+</span><span id="decimal_to_roman_numerals-199"><a href="#decimal_to_roman_numerals-199"><span class="linenos">199</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Decimal to Roman Numerals</span>
 </span><span id="decimal_to_roman_numerals-200"><a href="#decimal_to_roman_numerals-200"><span class="linenos">200</span></a>
 </span><span id="decimal_to_roman_numerals-201"><a href="#decimal_to_roman_numerals-201"><span class="linenos">201</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="decimal_to_roman_numerals-202"><a href="#decimal_to_roman_numerals-202"><span class="linenos">202</span></a><span class="sd">    | --- | --- |</span>
@@ -1192,7 +1192,7 @@
     </div>
     <a class="headerlink" href="#euclidian_norm"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="euclidian_norm-238"><a href="#euclidian_norm-238"><span class="linenos">238</span></a><span class="k">def</span> <span class="nf">euclidian_norm</span><span class="p">(</span><span class="n">maxEltAmt</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="euclidian_norm-239"><a href="#euclidian_norm-239"><span class="linenos">239</span></a>    <span class="sd">&quot;&quot;&quot;Euclidian norm or L2 norm of a vector</span>
+</span><span id="euclidian_norm-239"><a href="#euclidian_norm-239"><span class="linenos">239</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Euclidian norm or L2 norm of a vector</span>
 </span><span id="euclidian_norm-240"><a href="#euclidian_norm-240"><span class="linenos">240</span></a>
 </span><span id="euclidian_norm-241"><a href="#euclidian_norm-241"><span class="linenos">241</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="euclidian_norm-242"><a href="#euclidian_norm-242"><span class="linenos">242</span></a><span class="sd">    | --- | --- |</span>
@@ -1240,7 +1240,7 @@
     </div>
     <a class="headerlink" href="#factors"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="factors-254"><a href="#factors-254"><span class="linenos">254</span></a><span class="k">def</span> <span class="nf">factors</span><span class="p">(</span><span class="n">max_val</span><span class="o">=</span><span class="mi">1000</span><span class="p">):</span>
-</span><span id="factors-255"><a href="#factors-255"><span class="linenos">255</span></a>    <span class="sd">&quot;&quot;&quot;Factors of a number</span>
+</span><span id="factors-255"><a href="#factors-255"><span class="linenos">255</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Factors of a number</span>
 </span><span id="factors-256"><a href="#factors-256"><span class="linenos">256</span></a>
 </span><span id="factors-257"><a href="#factors-257"><span class="linenos">257</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="factors-258"><a href="#factors-258"><span class="linenos">258</span></a><span class="sd">    | --- | --- |</span>
@@ -1299,7 +1299,7 @@
     </div>
     <a class="headerlink" href="#geometric_mean"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="geometric_mean-281"><a href="#geometric_mean-281"><span class="linenos">281</span></a><span class="k">def</span> <span class="nf">geometric_mean</span><span class="p">(</span><span class="n">max_value</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">max_count</span><span class="o">=</span><span class="mi">4</span><span class="p">):</span>
-</span><span id="geometric_mean-282"><a href="#geometric_mean-282"><span class="linenos">282</span></a>    <span class="sd">&quot;&quot;&quot;Geometric Mean of N Numbers</span>
+</span><span id="geometric_mean-282"><a href="#geometric_mean-282"><span class="linenos">282</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Geometric Mean of N Numbers</span>
 </span><span id="geometric_mean-283"><a href="#geometric_mean-283"><span class="linenos">283</span></a>
 </span><span id="geometric_mean-284"><a href="#geometric_mean-284"><span class="linenos">284</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="geometric_mean-285"><a href="#geometric_mean-285"><span class="linenos">285</span></a><span class="sd">    | --- | --- |</span>
@@ -1353,7 +1353,7 @@
 </span><span id="geometric_progression-301"><a href="#geometric_progression-301"><span class="linenos">301</span></a>                          <span class="n">max_value</span><span class="o">=</span><span class="mi">12</span><span class="p">,</span>
 </span><span id="geometric_progression-302"><a href="#geometric_progression-302"><span class="linenos">302</span></a>                          <span class="n">n_term</span><span class="o">=</span><span class="mi">7</span><span class="p">,</span>
 </span><span id="geometric_progression-303"><a href="#geometric_progression-303"><span class="linenos">303</span></a>                          <span class="n">sum_term</span><span class="o">=</span><span class="mi">5</span><span class="p">):</span>
-</span><span id="geometric_progression-304"><a href="#geometric_progression-304"><span class="linenos">304</span></a>    <span class="sd">&quot;&quot;&quot;Geometric Progression</span>
+</span><span id="geometric_progression-304"><a href="#geometric_progression-304"><span class="linenos">304</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Geometric Progression</span>
 </span><span id="geometric_progression-305"><a href="#geometric_progression-305"><span class="linenos">305</span></a>
 </span><span id="geometric_progression-306"><a href="#geometric_progression-306"><span class="linenos">306</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="geometric_progression-307"><a href="#geometric_progression-307"><span class="linenos">307</span></a><span class="sd">    | --- | --- |</span>
@@ -1408,7 +1408,7 @@
     </div>
     <a class="headerlink" href="#harmonic_mean"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="harmonic_mean-326"><a href="#harmonic_mean-326"><span class="linenos">326</span></a><span class="k">def</span> <span class="nf">harmonic_mean</span><span class="p">(</span><span class="n">max_value</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">max_count</span><span class="o">=</span><span class="mi">4</span><span class="p">):</span>
-</span><span id="harmonic_mean-327"><a href="#harmonic_mean-327"><span class="linenos">327</span></a>    <span class="sd">&quot;&quot;&quot;Harmonic Mean of N Numbers</span>
+</span><span id="harmonic_mean-327"><a href="#harmonic_mean-327"><span class="linenos">327</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Harmonic Mean of N Numbers</span>
 </span><span id="harmonic_mean-328"><a href="#harmonic_mean-328"><span class="linenos">328</span></a>
 </span><span id="harmonic_mean-329"><a href="#harmonic_mean-329"><span class="linenos">329</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="harmonic_mean-330"><a href="#harmonic_mean-330"><span class="linenos">330</span></a><span class="sd">    | --- | --- |</span>
@@ -1421,7 +1421,7 @@
 </span><span id="harmonic_mean-337"><a href="#harmonic_mean-337"><span class="linenos">337</span></a>        <span class="nb">sum</span> <span class="o">+=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">num</span><span class="p">)</span>
 </span><span id="harmonic_mean-338"><a href="#harmonic_mean-338"><span class="linenos">338</span></a>    <span class="n">ans</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">num</span> <span class="o">/</span> <span class="nb">sum</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
 </span><span id="harmonic_mean-339"><a href="#harmonic_mean-339"><span class="linenos">339</span></a>
-</span><span id="harmonic_mean-340"><a href="#harmonic_mean-340"><span class="linenos">340</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Harmonic mean of $</span><span class="si">{</span><span class="n">count</span><span class="si">}</span><span class="s2">$ numbers $</span><span class="si">{</span><span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="n">nums</span><span class="p">))</span><span class="si">}</span><span class="s2"> = $&quot;</span>
+</span><span id="harmonic_mean-340"><a href="#harmonic_mean-340"><span class="linenos">340</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Harmonic mean of $</span><span class="si">{</span><span class="n">count</span><span class="si">}</span><span class="s2">$ numbers $</span><span class="si">{</span><span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">))</span><span class="si">}</span><span class="s2"> = $&quot;</span>
 </span><span id="harmonic_mean-341"><a href="#harmonic_mean-341"><span class="linenos">341</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">ans</span><span class="si">}</span><span class="s2">$&quot;</span>
 </span><span id="harmonic_mean-342"><a href="#harmonic_mean-342"><span class="linenos">342</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span></pre></div>
@@ -1459,7 +1459,7 @@
     </div>
     <a class="headerlink" href="#is_leap_year"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="is_leap_year-345"><a href="#is_leap_year-345"><span class="linenos">345</span></a><span class="k">def</span> <span class="nf">is_leap_year</span><span class="p">(</span><span class="n">minNumber</span><span class="o">=</span><span class="mi">1900</span><span class="p">,</span> <span class="n">max_number</span><span class="o">=</span><span class="mi">2099</span><span class="p">):</span>
-</span><span id="is_leap_year-346"><a href="#is_leap_year-346"><span class="linenos">346</span></a>    <span class="sd">&quot;&quot;&quot;Is Leap Year or Not</span>
+</span><span id="is_leap_year-346"><a href="#is_leap_year-346"><span class="linenos">346</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Is Leap Year or Not</span>
 </span><span id="is_leap_year-347"><a href="#is_leap_year-347"><span class="linenos">347</span></a>
 </span><span id="is_leap_year-348"><a href="#is_leap_year-348"><span class="linenos">348</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="is_leap_year-349"><a href="#is_leap_year-349"><span class="linenos">349</span></a><span class="sd">    | --- | --- |</span>
@@ -1478,7 +1478,7 @@
 </span><span id="is_leap_year-362"><a href="#is_leap_year-362"><span class="linenos">362</span></a>    <span class="k">else</span><span class="p">:</span>
 </span><span id="is_leap_year-363"><a href="#is_leap_year-363"><span class="linenos">363</span></a>        <span class="n">ans</span> <span class="o">=</span> <span class="kc">False</span>
 </span><span id="is_leap_year-364"><a href="#is_leap_year-364"><span class="linenos">364</span></a>
-</span><span id="is_leap_year-365"><a href="#is_leap_year-365"><span class="linenos">365</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">year</span><span class="si">}</span><span class="s2"> is</span><span class="si">{</span><span class="s1">&#39; not&#39;</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">ans</span> <span class="k">else</span> <span class="s1">&#39;&#39;</span><span class="si">}</span><span class="s2"> a leap year&quot;</span>
+</span><span id="is_leap_year-365"><a href="#is_leap_year-365"><span class="linenos">365</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">year</span><span class="si">}</span><span class="s2"> is</span><span class="si">{</span><span class="s1">&#39; not&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="ow">not</span><span class="w"> </span><span class="n">ans</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="s1">&#39;&#39;</span><span class="si">}</span><span class="s2"> a leap year&quot;</span>
 </span><span id="is_leap_year-366"><a href="#is_leap_year-366"><span class="linenos">366</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span></pre></div>
 
@@ -1515,7 +1515,7 @@
     </div>
     <a class="headerlink" href="#lcm"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="lcm-369"><a href="#lcm-369"><span class="linenos">369</span></a><span class="k">def</span> <span class="nf">lcm</span><span class="p">(</span><span class="n">max_val</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="lcm-370"><a href="#lcm-370"><span class="linenos">370</span></a>    <span class="sd">&quot;&quot;&quot;LCM (Least Common Multiple)</span>
+</span><span id="lcm-370"><a href="#lcm-370"><span class="linenos">370</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;LCM (Least Common Multiple)</span>
 </span><span id="lcm-371"><a href="#lcm-371"><span class="linenos">371</span></a>
 </span><span id="lcm-372"><a href="#lcm-372"><span class="linenos">372</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="lcm-373"><a href="#lcm-373"><span class="linenos">373</span></a><span class="sd">    | --- | --- |</span>
@@ -1568,7 +1568,7 @@
     </div>
     <a class="headerlink" href="#minutes_to_hours"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="minutes_to_hours-390"><a href="#minutes_to_hours-390"><span class="linenos">390</span></a><span class="k">def</span> <span class="nf">minutes_to_hours</span><span class="p">(</span><span class="n">max_minutes</span><span class="o">=</span><span class="mi">999</span><span class="p">):</span>
-</span><span id="minutes_to_hours-391"><a href="#minutes_to_hours-391"><span class="linenos">391</span></a>    <span class="sd">&quot;&quot;&quot;Convert minutes to hours and minutes</span>
+</span><span id="minutes_to_hours-391"><a href="#minutes_to_hours-391"><span class="linenos">391</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Convert minutes to hours and minutes</span>
 </span><span id="minutes_to_hours-392"><a href="#minutes_to_hours-392"><span class="linenos">392</span></a>
 </span><span id="minutes_to_hours-393"><a href="#minutes_to_hours-393"><span class="linenos">393</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="minutes_to_hours-394"><a href="#minutes_to_hours-394"><span class="linenos">394</span></a><span class="sd">    | --- | --- |</span>
@@ -1616,7 +1616,7 @@
     </div>
     <a class="headerlink" href="#prime_factors"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="prime_factors-406"><a href="#prime_factors-406"><span class="linenos">406</span></a><span class="k">def</span> <span class="nf">prime_factors</span><span class="p">(</span><span class="n">min_val</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_val</span><span class="o">=</span><span class="mi">200</span><span class="p">):</span>
-</span><span id="prime_factors-407"><a href="#prime_factors-407"><span class="linenos">407</span></a>    <span class="sd">&quot;&quot;&quot;Prime Factors</span>
+</span><span id="prime_factors-407"><a href="#prime_factors-407"><span class="linenos">407</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Prime Factors</span>
 </span><span id="prime_factors-408"><a href="#prime_factors-408"><span class="linenos">408</span></a>
 </span><span id="prime_factors-409"><a href="#prime_factors-409"><span class="linenos">409</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="prime_factors-410"><a href="#prime_factors-410"><span class="linenos">410</span></a><span class="sd">    | --- | --- |</span>
@@ -1638,7 +1638,7 @@
 </span><span id="prime_factors-426"><a href="#prime_factors-426"><span class="linenos">426</span></a>        <span class="n">factors</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
 </span><span id="prime_factors-427"><a href="#prime_factors-427"><span class="linenos">427</span></a>
 </span><span id="prime_factors-428"><a href="#prime_factors-428"><span class="linenos">428</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Find prime factors of $</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="s2">$&quot;</span>
-</span><span id="prime_factors-429"><a href="#prime_factors-429"><span class="linenos">429</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="n">factors</span><span class="p">))</span><span class="si">}</span><span class="s2">$&quot;</span>
+</span><span id="prime_factors-429"><a href="#prime_factors-429"><span class="linenos">429</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span><span class="w"> </span><span class="n">factors</span><span class="p">))</span><span class="si">}</span><span class="s2">$&quot;</span>
 </span><span id="prime_factors-430"><a href="#prime_factors-430"><span class="linenos">430</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span></pre></div>
 
@@ -1675,7 +1675,7 @@
     </div>
     <a class="headerlink" href="#product_of_scientific_notations"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="product_of_scientific_notations-433"><a href="#product_of_scientific_notations-433"><span class="linenos">433</span></a><span class="k">def</span> <span class="nf">product_of_scientific_notations</span><span class="p">(</span><span class="n">min_exp_val</span><span class="o">=-</span><span class="mi">100</span><span class="p">,</span> <span class="n">max_exp_val</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
-</span><span id="product_of_scientific_notations-434"><a href="#product_of_scientific_notations-434"><span class="linenos">434</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Product of scientific notations</span>
+</span><span id="product_of_scientific_notations-434"><a href="#product_of_scientific_notations-434"><span class="linenos">434</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Product of scientific notations</span>
 </span><span id="product_of_scientific_notations-435"><a href="#product_of_scientific_notations-435"><span class="linenos">435</span></a>
 </span><span id="product_of_scientific_notations-436"><a href="#product_of_scientific_notations-436"><span class="linenos">436</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="product_of_scientific_notations-437"><a href="#product_of_scientific_notations-437"><span class="linenos">437</span></a><span class="sd">    | --- | --- |</span>
@@ -1692,7 +1692,7 @@
 </span><span id="product_of_scientific_notations-448"><a href="#product_of_scientific_notations-448"><span class="linenos">448</span></a>        <span class="n">c</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
 </span><span id="product_of_scientific_notations-449"><a href="#product_of_scientific_notations-449"><span class="linenos">449</span></a>
 </span><span id="product_of_scientific_notations-450"><a href="#product_of_scientific_notations-450"><span class="linenos">450</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">rf</span><span class="s2">&quot;Product of scientific notations $</span><span class="si">{</span><span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="si">}</span><span class="s2"> \times 10^</span><span class="se">{{</span><span class="si">{</span><span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="si">}</span><span class="se">}}</span><span class="s2">$ and $</span><span class="si">{</span><span class="n">b</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="si">}</span><span class="s2"> \times 10^</span><span class="se">{{</span><span class="si">{</span><span class="n">b</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="si">}</span><span class="se">}}</span><span class="s2"> = $&quot;</span>
-</span><span id="product_of_scientific_notations-451"><a href="#product_of_scientific_notations-451"><span class="linenos">451</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;$</span><span class="si">{</span><span class="nb">round</span><span class="p">(</span><span class="n">c</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="mi">2</span><span class="p">)</span><span class="si">}</span><span class="s1"> \times 10^</span><span class="se">{{</span><span class="si">{</span><span class="n">c</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="si">}</span><span class="se">}}</span><span class="s1">$&#39;</span>
+</span><span id="product_of_scientific_notations-451"><a href="#product_of_scientific_notations-451"><span class="linenos">451</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">rf</span><span class="s1">&#39;$</span><span class="si">{</span><span class="nb">round</span><span class="p">(</span><span class="n">c</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="si">}</span><span class="s1"> \times 10^</span><span class="se">{{</span><span class="si">{</span><span class="n">c</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="si">}</span><span class="se">}}</span><span class="s1">$&#39;</span>
 </span><span id="product_of_scientific_notations-452"><a href="#product_of_scientific_notations-452"><span class="linenos">452</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span></pre></div>
 
@@ -1729,7 +1729,7 @@
     </div>
     <a class="headerlink" href="#profit_loss_percent"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="profit_loss_percent-455"><a href="#profit_loss_percent-455"><span class="linenos">455</span></a><span class="k">def</span> <span class="nf">profit_loss_percent</span><span class="p">(</span><span class="n">max_cp</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span> <span class="n">max_sp</span><span class="o">=</span><span class="mi">1000</span><span class="p">):</span>
-</span><span id="profit_loss_percent-456"><a href="#profit_loss_percent-456"><span class="linenos">456</span></a>    <span class="sd">&quot;&quot;&quot;Profit or Loss Percent</span>
+</span><span id="profit_loss_percent-456"><a href="#profit_loss_percent-456"><span class="linenos">456</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Profit or Loss Percent</span>
 </span><span id="profit_loss_percent-457"><a href="#profit_loss_percent-457"><span class="linenos">457</span></a>
 </span><span id="profit_loss_percent-458"><a href="#profit_loss_percent-458"><span class="linenos">458</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="profit_loss_percent-459"><a href="#profit_loss_percent-459"><span class="linenos">459</span></a><span class="sd">    | --- | --- |</span>
@@ -1781,11 +1781,11 @@
     </div>
     <a class="headerlink" href="#quotient_of_power_same_base"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="quotient_of_power_same_base-475"><a href="#quotient_of_power_same_base-475"><span class="linenos">475</span></a><span class="k">def</span> <span class="nf">quotient_of_power_same_base</span><span class="p">(</span><span class="n">max_base</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">max_power</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="quotient_of_power_same_base-476"><a href="#quotient_of_power_same_base-476"><span class="linenos">476</span></a>    <span class="sd">&quot;&quot;&quot;Quotient of Powers with Same Base</span>
+</span><span id="quotient_of_power_same_base-476"><a href="#quotient_of_power_same_base-476"><span class="linenos">476</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Quotient of Powers with Same Base</span>
 </span><span id="quotient_of_power_same_base-477"><a href="#quotient_of_power_same_base-477"><span class="linenos">477</span></a>
 </span><span id="quotient_of_power_same_base-478"><a href="#quotient_of_power_same_base-478"><span class="linenos">478</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="quotient_of_power_same_base-479"><a href="#quotient_of_power_same_base-479"><span class="linenos">479</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="quotient_of_power_same_base-480"><a href="#quotient_of_power_same_base-480"><span class="linenos">480</span></a><span class="sd">    | The Quotient of $5^{6}$ and $5^{8} = $5^{6-8} = 5^{-2}$ | $0.04$ |</span>
+</span><span id="quotient_of_power_same_base-480"><a href="#quotient_of_power_same_base-480"><span class="linenos">480</span></a><span class="sd">    | The Quotient of $5^{6}$ and $5^{8} = 5^{6-8} = 5^{-2}$ | $0.04$ |</span>
 </span><span id="quotient_of_power_same_base-481"><a href="#quotient_of_power_same_base-481"><span class="linenos">481</span></a><span class="sd">    &quot;&quot;&quot;</span>
 </span><span id="quotient_of_power_same_base-482"><a href="#quotient_of_power_same_base-482"><span class="linenos">482</span></a>    <span class="n">base</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_base</span><span class="p">)</span>
 </span><span id="quotient_of_power_same_base-483"><a href="#quotient_of_power_same_base-483"><span class="linenos">483</span></a>    <span class="n">power1</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">max_power</span><span class="p">)</span>
@@ -1794,7 +1794,7 @@
 </span><span id="quotient_of_power_same_base-486"><a href="#quotient_of_power_same_base-486"><span class="linenos">486</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="n">base</span> <span class="o">**</span> <span class="n">step</span>
 </span><span id="quotient_of_power_same_base-487"><a href="#quotient_of_power_same_base-487"><span class="linenos">487</span></a>
 </span><span id="quotient_of_power_same_base-488"><a href="#quotient_of_power_same_base-488"><span class="linenos">488</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;The Quotient of $</span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2">^</span><span class="se">{{</span><span class="si">{</span><span class="n">power1</span><span class="si">}</span><span class="se">}}</span><span class="s2">$ and $</span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2">^</span><span class="se">{{</span><span class="si">{</span><span class="n">power2</span><span class="si">}</span><span class="se">}}</span><span class="s2"> = &quot;</span> \
-</span><span id="quotient_of_power_same_base-489"><a href="#quotient_of_power_same_base-489"><span class="linenos">489</span></a>        <span class="sa">f</span><span class="s2">&quot;$</span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2">^</span><span class="se">{{</span><span class="si">{</span><span class="n">power1</span><span class="si">}</span><span class="s2">-</span><span class="si">{</span><span class="n">power2</span><span class="si">}</span><span class="se">}}</span><span class="s2"> = </span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2">^</span><span class="se">{{</span><span class="si">{</span><span class="n">step</span><span class="si">}</span><span class="se">}}</span><span class="s2">$&quot;</span>
+</span><span id="quotient_of_power_same_base-489"><a href="#quotient_of_power_same_base-489"><span class="linenos">489</span></a>        <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2">^</span><span class="se">{{</span><span class="si">{</span><span class="n">power1</span><span class="si">}</span><span class="s2">-</span><span class="si">{</span><span class="n">power2</span><span class="si">}</span><span class="se">}}</span><span class="s2"> = </span><span class="si">{</span><span class="n">base</span><span class="si">}</span><span class="s2">^</span><span class="se">{{</span><span class="si">{</span><span class="n">step</span><span class="si">}</span><span class="se">}}</span><span class="s2">$&quot;</span>
 </span><span id="quotient_of_power_same_base-490"><a href="#quotient_of_power_same_base-490"><span class="linenos">490</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;$</span><span class="si">{</span><span class="n">solution</span><span class="si">}</span><span class="s1">$&#39;</span>
 </span></pre></div>
 
@@ -1810,7 +1810,7 @@
 </thead>
 <tbody>
 <tr>
-  <td>The Quotient of $5^{6}$ and $5^{8} = $5^{6-8} = 5^{-2}$</td>
+  <td>The Quotient of $5^{6}$ and $5^{8} = 5^{6-8} = 5^{-2}$</td>
   <td>$0.04$</td>
 </tr>
 </tbody>
@@ -1831,7 +1831,7 @@
     </div>
     <a class="headerlink" href="#quotient_of_power_same_power"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="quotient_of_power_same_power-493"><a href="#quotient_of_power_same_power-493"><span class="linenos">493</span></a><span class="k">def</span> <span class="nf">quotient_of_power_same_power</span><span class="p">(</span><span class="n">max_base</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">max_power</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="quotient_of_power_same_power-494"><a href="#quotient_of_power_same_power-494"><span class="linenos">494</span></a>    <span class="sd">&quot;&quot;&quot;Quotient of Powers with Same Power</span>
+</span><span id="quotient_of_power_same_power-494"><a href="#quotient_of_power_same_power-494"><span class="linenos">494</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Quotient of Powers with Same Power</span>
 </span><span id="quotient_of_power_same_power-495"><a href="#quotient_of_power_same_power-495"><span class="linenos">495</span></a>
 </span><span id="quotient_of_power_same_power-496"><a href="#quotient_of_power_same_power-496"><span class="linenos">496</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="quotient_of_power_same_power-497"><a href="#quotient_of_power_same_power-497"><span class="linenos">497</span></a><span class="sd">    | --- | --- |</span>
@@ -1881,11 +1881,11 @@
     </div>
     <a class="headerlink" href="#set_operation"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="set_operation-511"><a href="#set_operation-511"><span class="linenos">511</span></a><span class="k">def</span> <span class="nf">set_operation</span><span class="p">(</span><span class="n">min_size</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">max_size</span><span class="o">=</span><span class="mi">7</span><span class="p">):</span>
-</span><span id="set_operation-512"><a href="#set_operation-512"><span class="linenos">512</span></a>    <span class="sd">&quot;&quot;&quot;Union, Intersection, Difference of Two Sets</span>
+</span><span id="set_operation-512"><a href="#set_operation-512"><span class="linenos">512</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Union, Intersection, Difference of Two Sets</span>
 </span><span id="set_operation-513"><a href="#set_operation-513"><span class="linenos">513</span></a>
 </span><span id="set_operation-514"><a href="#set_operation-514"><span class="linenos">514</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="set_operation-515"><a href="#set_operation-515"><span class="linenos">515</span></a><span class="sd">    | --- | --- |</span>
-</span><span id="set_operation-516"><a href="#set_operation-516"><span class="linenos">516</span></a><span class="sd">    | Given the two sets $a={1, 2, 4, 5}$, $b={8, 1, 2}. Find the Union, intersection, a-b, b-a, and symmetric difference | Union is ${1, 2, 4, 5, 8}$. Intersection is ${1, 2}$, a-b is ${4, 5}$, b-a is ${8}$. Symmetric difference is ${4, 5, 8}$. |</span>
+</span><span id="set_operation-516"><a href="#set_operation-516"><span class="linenos">516</span></a><span class="sd">    | Given the two sets $a={1, 2, 4, 5}$, $b={8, 1, 2}$. Find the Union, intersection, $a-b$, $b-a$, and symmetric difference | Union is ${1, 2, 4, 5, 8}$. Intersection is ${1, 2}$, $a-b$ is ${4, 5}$, $b-a$ is ${8}$. Symmetric difference is ${4, 5, 8}$. |</span>
 </span><span id="set_operation-517"><a href="#set_operation-517"><span class="linenos">517</span></a><span class="sd">    &quot;&quot;&quot;</span>
 </span><span id="set_operation-518"><a href="#set_operation-518"><span class="linenos">518</span></a>    <span class="n">number_variables_a</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="n">min_size</span><span class="p">,</span> <span class="n">max_size</span><span class="p">)</span>
 </span><span id="set_operation-519"><a href="#set_operation-519"><span class="linenos">519</span></a>    <span class="n">number_variables_b</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="n">min_size</span><span class="p">,</span> <span class="n">max_size</span><span class="p">)</span>
@@ -1898,10 +1898,10 @@
 </span><span id="set_operation-526"><a href="#set_operation-526"><span class="linenos">526</span></a>    <span class="n">a</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
 </span><span id="set_operation-527"><a href="#set_operation-527"><span class="linenos">527</span></a>    <span class="n">b</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
 </span><span id="set_operation-528"><a href="#set_operation-528"><span class="linenos">528</span></a>
-</span><span id="set_operation-529"><a href="#set_operation-529"><span class="linenos">529</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Given the two sets $a=</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="s2">$, $b=</span><span class="si">{</span><span class="n">b</span><span class="si">}</span><span class="s2">. &quot;</span> <span class="o">+</span> \
-</span><span id="set_operation-530"><a href="#set_operation-530"><span class="linenos">530</span></a>        <span class="s2">&quot;Find the Union, intersection, a-b, b-a, and symmetric difference&quot;</span>
+</span><span id="set_operation-529"><a href="#set_operation-529"><span class="linenos">529</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Given the two sets $a=</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="s2">$, $b=</span><span class="si">{</span><span class="n">b</span><span class="si">}</span><span class="s2">$. &quot;</span> <span class="o">+</span> \
+</span><span id="set_operation-530"><a href="#set_operation-530"><span class="linenos">530</span></a>        <span class="s2">&quot;Find the Union, intersection, $a-b$, $b-a$, and symmetric difference&quot;</span>
 </span><span id="set_operation-531"><a href="#set_operation-531"><span class="linenos">531</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Union is $</span><span class="si">{</span><span class="n">a</span><span class="o">.</span><span class="n">union</span><span class="p">(</span><span class="n">b</span><span class="p">)</span><span class="si">}</span><span class="s2">$. Intersection is $</span><span class="si">{</span><span class="n">a</span><span class="o">.</span><span class="n">intersection</span><span class="p">(</span><span class="n">b</span><span class="p">)</span><span class="si">}</span><span class="s2">$&quot;</span> <span class="o">+</span> \
-</span><span id="set_operation-532"><a href="#set_operation-532"><span class="linenos">532</span></a>        <span class="sa">f</span><span class="s2">&quot;, a-b is $</span><span class="si">{</span><span class="n">a</span><span class="o">.</span><span class="n">difference</span><span class="p">(</span><span class="n">b</span><span class="p">)</span><span class="si">}</span><span class="s2">$, b-a is $</span><span class="si">{</span><span class="n">b</span><span class="o">.</span><span class="n">difference</span><span class="p">(</span><span class="n">a</span><span class="p">)</span><span class="si">}</span><span class="s2">$.&quot;</span> <span class="o">+</span> \
+</span><span id="set_operation-532"><a href="#set_operation-532"><span class="linenos">532</span></a>        <span class="sa">f</span><span class="s2">&quot;, $a-b$ is $</span><span class="si">{</span><span class="n">a</span><span class="o">.</span><span class="n">difference</span><span class="p">(</span><span class="n">b</span><span class="p">)</span><span class="si">}</span><span class="s2">$, $b-a$ is $</span><span class="si">{</span><span class="n">b</span><span class="o">.</span><span class="n">difference</span><span class="p">(</span><span class="n">a</span><span class="p">)</span><span class="si">}</span><span class="s2">$.&quot;</span> <span class="o">+</span> \
 </span><span id="set_operation-533"><a href="#set_operation-533"><span class="linenos">533</span></a>        <span class="sa">f</span><span class="s2">&quot; Symmetric difference is $</span><span class="si">{</span><span class="n">a</span><span class="o">.</span><span class="n">symmetric_difference</span><span class="p">(</span><span class="n">b</span><span class="p">)</span><span class="si">}</span><span class="s2">$.&quot;</span>
 </span><span id="set_operation-534"><a href="#set_operation-534"><span class="linenos">534</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span></pre></div>
@@ -1918,8 +1918,8 @@
 </thead>
 <tbody>
 <tr>
-  <td>Given the two sets $a={1, 2, 4, 5}$, $b={8, 1, 2}. Find the Union, intersection, a-b, b-a, and symmetric difference</td>
-  <td>Union is ${1, 2, 4, 5, 8}$. Intersection is ${1, 2}$, a-b is ${4, 5}$, b-a is ${8}$. Symmetric difference is ${4, 5, 8}$.</td>
+  <td>Given the two sets $a={1, 2, 4, 5}$, $b={8, 1, 2}$. Find the Union, intersection, $a-b$, $b-a$, and symmetric difference</td>
+  <td>Union is ${1, 2, 4, 5, 8}$. Intersection is ${1, 2}$, $a-b$ is ${4, 5}$, $b-a$ is ${8}$. Symmetric difference is ${4, 5, 8}$.</td>
 </tr>
 </tbody>
 </table>
@@ -1939,7 +1939,7 @@
     </div>
     <a class="headerlink" href="#signum_function"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="signum_function-537"><a href="#signum_function-537"><span class="linenos">537</span></a><span class="k">def</span> <span class="nf">signum_function</span><span class="p">(</span><span class="nb">min</span><span class="o">=-</span><span class="mi">999</span><span class="p">,</span> <span class="nb">max</span><span class="o">=</span><span class="mi">999</span><span class="p">):</span>
-</span><span id="signum_function-538"><a href="#signum_function-538"><span class="linenos">538</span></a>    <span class="sd">&quot;&quot;&quot;Signum Function</span>
+</span><span id="signum_function-538"><a href="#signum_function-538"><span class="linenos">538</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Signum Function</span>
 </span><span id="signum_function-539"><a href="#signum_function-539"><span class="linenos">539</span></a>
 </span><span id="signum_function-540"><a href="#signum_function-540"><span class="linenos">540</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="signum_function-541"><a href="#signum_function-541"><span class="linenos">541</span></a><span class="sd">    | --- | --- |</span>
@@ -1990,7 +1990,7 @@
     </div>
     <a class="headerlink" href="#surds_comparison"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="surds_comparison-556"><a href="#surds_comparison-556"><span class="linenos">556</span></a><span class="k">def</span> <span class="nf">surds_comparison</span><span class="p">(</span><span class="n">max_value</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">max_root</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="surds_comparison-557"><a href="#surds_comparison-557"><span class="linenos">557</span></a>    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Comparing Surds</span>
+</span><span id="surds_comparison-557"><a href="#surds_comparison-557"><span class="linenos">557</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Comparing Surds</span>
 </span><span id="surds_comparison-558"><a href="#surds_comparison-558"><span class="linenos">558</span></a>
 </span><span id="surds_comparison-559"><a href="#surds_comparison-559"><span class="linenos">559</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="surds_comparison-560"><a href="#surds_comparison-560"><span class="linenos">560</span></a><span class="sd">    | --- | --- |</span>
@@ -2152,7 +2152,7 @@
                         if (doc.annotation)
                             heading += `<span class="annotation">${doc.annotation}</span>`;
                         if (doc.default_value)
-                            heading += `<span class="default_value">${doc.default_value}</span>`;
+                            heading += `<span class="default_value"> = ${doc.default_value}</span>`;
                         break;
                     default:
                         heading = `<span class="name">${doc.fullname}</span>`;
diff --git a/docs/mathgenerator/statistics.html b/docs/mathgenerator/statistics.html
index 776dd12..d8840c1 100644
--- a/docs/mathgenerator/statistics.html
+++ b/docs/mathgenerator/statistics.html
@@ -3,14 +3,14 @@
 <head>
     <meta charset="utf-8">
     <meta name="viewport" content="width=device-width, initial-scale=1">
-    <meta name="generator" content="pdoc 12.3.0"/>
+    <meta name="generator" content="pdoc 13.1.1"/>
     <title>mathgenerator.statistics API documentation</title>
 
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@@ -50,8 +50,8 @@
 
 
 
-        <h2>API Documentation</h2>
-            <ul class="memberlist">
+            <h2>API Documentation</h2>
+                <ul class="memberlist">
             <li>
                     <a class="function" href="#combinations">combinations</a>
             </li>
@@ -99,7 +99,7 @@
 </span><span id="L-3"><a href="#L-3"><span class="linenos">  3</span></a>
 </span><span id="L-4"><a href="#L-4"><span class="linenos">  4</span></a>
 </span><span id="L-5"><a href="#L-5"><span class="linenos">  5</span></a><span class="k">def</span> <span class="nf">combinations</span><span class="p">(</span><span class="n">max_lengthgth</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="L-6"><a href="#L-6"><span class="linenos">  6</span></a>    <span class="sd">&quot;&quot;&quot;Combinations of Objects</span>
+</span><span id="L-6"><a href="#L-6"><span class="linenos">  6</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Combinations of Objects</span>
 </span><span id="L-7"><a href="#L-7"><span class="linenos">  7</span></a>
 </span><span id="L-8"><a href="#L-8"><span class="linenos">  8</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-9"><a href="#L-9"><span class="linenos">  9</span></a><span class="sd">    | --- | --- |</span>
@@ -116,7 +116,7 @@
 </span><span id="L-20"><a href="#L-20"><span class="linenos"> 20</span></a>
 </span><span id="L-21"><a href="#L-21"><span class="linenos"> 21</span></a>
 </span><span id="L-22"><a href="#L-22"><span class="linenos"> 22</span></a><span class="k">def</span> <span class="nf">conditional_probability</span><span class="p">():</span>
-</span><span id="L-23"><a href="#L-23"><span class="linenos"> 23</span></a>    <span class="sd">&quot;&quot;&quot;Conditional Probability</span>
+</span><span id="L-23"><a href="#L-23"><span class="linenos"> 23</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Conditional Probability</span>
 </span><span id="L-24"><a href="#L-24"><span class="linenos"> 24</span></a>
 </span><span id="L-25"><a href="#L-25"><span class="linenos"> 25</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-26"><a href="#L-26"><span class="linenos"> 26</span></a><span class="sd">    | --- | --- |</span>
@@ -146,7 +146,7 @@
 </span><span id="L-50"><a href="#L-50"><span class="linenos"> 50</span></a>
 </span><span id="L-51"><a href="#L-51"><span class="linenos"> 51</span></a>
 </span><span id="L-52"><a href="#L-52"><span class="linenos"> 52</span></a><span class="k">def</span> <span class="nf">confidence_interval</span><span class="p">():</span>
-</span><span id="L-53"><a href="#L-53"><span class="linenos"> 53</span></a>    <span class="sd">&quot;&quot;&quot;Confidence interval For sample S</span>
+</span><span id="L-53"><a href="#L-53"><span class="linenos"> 53</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Confidence interval For sample S</span>
 </span><span id="L-54"><a href="#L-54"><span class="linenos"> 54</span></a>
 </span><span id="L-55"><a href="#L-55"><span class="linenos"> 55</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-56"><a href="#L-56"><span class="linenos"> 56</span></a><span class="sd">    | --- | --- |</span>
@@ -184,7 +184,7 @@
 </span><span id="L-88"><a href="#L-88"><span class="linenos"> 88</span></a>
 </span><span id="L-89"><a href="#L-89"><span class="linenos"> 89</span></a>
 </span><span id="L-90"><a href="#L-90"><span class="linenos"> 90</span></a><span class="k">def</span> <span class="nf">data_summary</span><span class="p">(</span><span class="n">number_values</span><span class="o">=</span><span class="mi">15</span><span class="p">,</span> <span class="n">min_val</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">max_val</span><span class="o">=</span><span class="mi">50</span><span class="p">):</span>
-</span><span id="L-91"><a href="#L-91"><span class="linenos"> 91</span></a>    <span class="sd">&quot;&quot;&quot;Mean, Standard Deviation and Variance</span>
+</span><span id="L-91"><a href="#L-91"><span class="linenos"> 91</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Mean, Standard Deviation and Variance</span>
 </span><span id="L-92"><a href="#L-92"><span class="linenos"> 92</span></a>
 </span><span id="L-93"><a href="#L-93"><span class="linenos"> 93</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-94"><a href="#L-94"><span class="linenos"> 94</span></a><span class="sd">    | --- | --- |</span>
@@ -206,13 +206,13 @@
 </span><span id="L-110"><a href="#L-110"><span class="linenos">110</span></a>    <span class="n">standardDeviation</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">var</span> <span class="o">/</span> <span class="n">number_values</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
 </span><span id="L-111"><a href="#L-111"><span class="linenos">111</span></a>    <span class="n">variance</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="n">var</span> <span class="o">/</span> <span class="n">number_values</span><span class="p">)</span> <span class="o">**</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
 </span><span id="L-112"><a href="#L-112"><span class="linenos">112</span></a>
-</span><span id="L-113"><a href="#L-113"><span class="linenos">113</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Find the mean,standard deviation and variance for the data $</span><span class="si">{</span><span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="n">random_list</span><span class="p">))</span><span class="si">}</span><span class="s2">$&quot;</span>
+</span><span id="L-113"><a href="#L-113"><span class="linenos">113</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Find the mean,standard deviation and variance for the data $</span><span class="si">{</span><span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span><span class="w"> </span><span class="n">random_list</span><span class="p">))</span><span class="si">}</span><span class="s2">$&quot;</span>
 </span><span id="L-114"><a href="#L-114"><span class="linenos">114</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;The Mean is $</span><span class="si">{</span><span class="n">mean</span><span class="si">}</span><span class="s2">$, Standard Deviation is $</span><span class="si">{</span><span class="n">standardDeviation</span><span class="si">}</span><span class="s2">$, Variance is $</span><span class="si">{</span><span class="n">variance</span><span class="si">}</span><span class="s2">$&quot;</span>
 </span><span id="L-115"><a href="#L-115"><span class="linenos">115</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span><span id="L-116"><a href="#L-116"><span class="linenos">116</span></a>
 </span><span id="L-117"><a href="#L-117"><span class="linenos">117</span></a>
 </span><span id="L-118"><a href="#L-118"><span class="linenos">118</span></a><span class="k">def</span> <span class="nf">dice_sum_probability</span><span class="p">(</span><span class="n">max_dice</span><span class="o">=</span><span class="mi">3</span><span class="p">):</span>
-</span><span id="L-119"><a href="#L-119"><span class="linenos">119</span></a>    <span class="sd">&quot;&quot;&quot;Probability of a certain sum appearing on faces of dice</span>
+</span><span id="L-119"><a href="#L-119"><span class="linenos">119</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Probability of a certain sum appearing on faces of dice</span>
 </span><span id="L-120"><a href="#L-120"><span class="linenos">120</span></a>
 </span><span id="L-121"><a href="#L-121"><span class="linenos">121</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-122"><a href="#L-122"><span class="linenos">122</span></a><span class="sd">    | --- | --- |</span>
@@ -242,7 +242,7 @@
 </span><span id="L-146"><a href="#L-146"><span class="linenos">146</span></a>
 </span><span id="L-147"><a href="#L-147"><span class="linenos">147</span></a>
 </span><span id="L-148"><a href="#L-148"><span class="linenos">148</span></a><span class="k">def</span> <span class="nf">mean_median</span><span class="p">(</span><span class="n">max_length</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="L-149"><a href="#L-149"><span class="linenos">149</span></a>    <span class="sd">&quot;&quot;&quot;Mean and Median</span>
+</span><span id="L-149"><a href="#L-149"><span class="linenos">149</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Mean and Median</span>
 </span><span id="L-150"><a href="#L-150"><span class="linenos">150</span></a>
 </span><span id="L-151"><a href="#L-151"><span class="linenos">151</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-152"><a href="#L-152"><span class="linenos">152</span></a><span class="sd">    | --- | --- |</span>
@@ -262,7 +262,7 @@
 </span><span id="L-166"><a href="#L-166"><span class="linenos">166</span></a>
 </span><span id="L-167"><a href="#L-167"><span class="linenos">167</span></a>
 </span><span id="L-168"><a href="#L-168"><span class="linenos">168</span></a><span class="k">def</span> <span class="nf">permutation</span><span class="p">(</span><span class="n">max_lengthgth</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="L-169"><a href="#L-169"><span class="linenos">169</span></a>    <span class="sd">&quot;&quot;&quot;Permutations</span>
+</span><span id="L-169"><a href="#L-169"><span class="linenos">169</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Permutations</span>
 </span><span id="L-170"><a href="#L-170"><span class="linenos">170</span></a>
 </span><span id="L-171"><a href="#L-171"><span class="linenos">171</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="L-172"><a href="#L-172"><span class="linenos">172</span></a><span class="sd">    | --- | --- |</span>
@@ -290,7 +290,7 @@
     </div>
     <a class="headerlink" href="#combinations"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="combinations-6"><a href="#combinations-6"><span class="linenos"> 6</span></a><span class="k">def</span> <span class="nf">combinations</span><span class="p">(</span><span class="n">max_lengthgth</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="combinations-7"><a href="#combinations-7"><span class="linenos"> 7</span></a>    <span class="sd">&quot;&quot;&quot;Combinations of Objects</span>
+</span><span id="combinations-7"><a href="#combinations-7"><span class="linenos"> 7</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Combinations of Objects</span>
 </span><span id="combinations-8"><a href="#combinations-8"><span class="linenos"> 8</span></a>
 </span><span id="combinations-9"><a href="#combinations-9"><span class="linenos"> 9</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="combinations-10"><a href="#combinations-10"><span class="linenos">10</span></a><span class="sd">    | --- | --- |</span>
@@ -339,7 +339,7 @@
     </div>
     <a class="headerlink" href="#conditional_probability"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="conditional_probability-23"><a href="#conditional_probability-23"><span class="linenos">23</span></a><span class="k">def</span> <span class="nf">conditional_probability</span><span class="p">():</span>
-</span><span id="conditional_probability-24"><a href="#conditional_probability-24"><span class="linenos">24</span></a>    <span class="sd">&quot;&quot;&quot;Conditional Probability</span>
+</span><span id="conditional_probability-24"><a href="#conditional_probability-24"><span class="linenos">24</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Conditional Probability</span>
 </span><span id="conditional_probability-25"><a href="#conditional_probability-25"><span class="linenos">25</span></a>
 </span><span id="conditional_probability-26"><a href="#conditional_probability-26"><span class="linenos">26</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="conditional_probability-27"><a href="#conditional_probability-27"><span class="linenos">27</span></a><span class="sd">    | --- | --- |</span>
@@ -401,7 +401,7 @@
     </div>
     <a class="headerlink" href="#confidence_interval"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="confidence_interval-53"><a href="#confidence_interval-53"><span class="linenos">53</span></a><span class="k">def</span> <span class="nf">confidence_interval</span><span class="p">():</span>
-</span><span id="confidence_interval-54"><a href="#confidence_interval-54"><span class="linenos">54</span></a>    <span class="sd">&quot;&quot;&quot;Confidence interval For sample S</span>
+</span><span id="confidence_interval-54"><a href="#confidence_interval-54"><span class="linenos">54</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Confidence interval For sample S</span>
 </span><span id="confidence_interval-55"><a href="#confidence_interval-55"><span class="linenos">55</span></a>
 </span><span id="confidence_interval-56"><a href="#confidence_interval-56"><span class="linenos">56</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="confidence_interval-57"><a href="#confidence_interval-57"><span class="linenos">57</span></a><span class="sd">    | --- | --- |</span>
@@ -471,7 +471,7 @@
     </div>
     <a class="headerlink" href="#data_summary"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="data_summary-91"><a href="#data_summary-91"><span class="linenos"> 91</span></a><span class="k">def</span> <span class="nf">data_summary</span><span class="p">(</span><span class="n">number_values</span><span class="o">=</span><span class="mi">15</span><span class="p">,</span> <span class="n">min_val</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">max_val</span><span class="o">=</span><span class="mi">50</span><span class="p">):</span>
-</span><span id="data_summary-92"><a href="#data_summary-92"><span class="linenos"> 92</span></a>    <span class="sd">&quot;&quot;&quot;Mean, Standard Deviation and Variance</span>
+</span><span id="data_summary-92"><a href="#data_summary-92"><span class="linenos"> 92</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Mean, Standard Deviation and Variance</span>
 </span><span id="data_summary-93"><a href="#data_summary-93"><span class="linenos"> 93</span></a>
 </span><span id="data_summary-94"><a href="#data_summary-94"><span class="linenos"> 94</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="data_summary-95"><a href="#data_summary-95"><span class="linenos"> 95</span></a><span class="sd">    | --- | --- |</span>
@@ -493,7 +493,7 @@
 </span><span id="data_summary-111"><a href="#data_summary-111"><span class="linenos">111</span></a>    <span class="n">standardDeviation</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">var</span> <span class="o">/</span> <span class="n">number_values</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
 </span><span id="data_summary-112"><a href="#data_summary-112"><span class="linenos">112</span></a>    <span class="n">variance</span> <span class="o">=</span> <span class="nb">round</span><span class="p">((</span><span class="n">var</span> <span class="o">/</span> <span class="n">number_values</span><span class="p">)</span> <span class="o">**</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
 </span><span id="data_summary-113"><a href="#data_summary-113"><span class="linenos">113</span></a>
-</span><span id="data_summary-114"><a href="#data_summary-114"><span class="linenos">114</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Find the mean,standard deviation and variance for the data $</span><span class="si">{</span><span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="n">random_list</span><span class="p">))</span><span class="si">}</span><span class="s2">$&quot;</span>
+</span><span id="data_summary-114"><a href="#data_summary-114"><span class="linenos">114</span></a>    <span class="n">problem</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Find the mean,standard deviation and variance for the data $</span><span class="si">{</span><span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span><span class="w"> </span><span class="n">random_list</span><span class="p">))</span><span class="si">}</span><span class="s2">$&quot;</span>
 </span><span id="data_summary-115"><a href="#data_summary-115"><span class="linenos">115</span></a>    <span class="n">solution</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;The Mean is $</span><span class="si">{</span><span class="n">mean</span><span class="si">}</span><span class="s2">$, Standard Deviation is $</span><span class="si">{</span><span class="n">standardDeviation</span><span class="si">}</span><span class="s2">$, Variance is $</span><span class="si">{</span><span class="n">variance</span><span class="si">}</span><span class="s2">$&quot;</span>
 </span><span id="data_summary-116"><a href="#data_summary-116"><span class="linenos">116</span></a>    <span class="k">return</span> <span class="n">problem</span><span class="p">,</span> <span class="n">solution</span>
 </span></pre></div>
@@ -531,7 +531,7 @@
     </div>
     <a class="headerlink" href="#dice_sum_probability"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="dice_sum_probability-119"><a href="#dice_sum_probability-119"><span class="linenos">119</span></a><span class="k">def</span> <span class="nf">dice_sum_probability</span><span class="p">(</span><span class="n">max_dice</span><span class="o">=</span><span class="mi">3</span><span class="p">):</span>
-</span><span id="dice_sum_probability-120"><a href="#dice_sum_probability-120"><span class="linenos">120</span></a>    <span class="sd">&quot;&quot;&quot;Probability of a certain sum appearing on faces of dice</span>
+</span><span id="dice_sum_probability-120"><a href="#dice_sum_probability-120"><span class="linenos">120</span></a><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Probability of a certain sum appearing on faces of dice</span>
 </span><span id="dice_sum_probability-121"><a href="#dice_sum_probability-121"><span class="linenos">121</span></a>
 </span><span id="dice_sum_probability-122"><a href="#dice_sum_probability-122"><span class="linenos">122</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="dice_sum_probability-123"><a href="#dice_sum_probability-123"><span class="linenos">123</span></a><span class="sd">    | --- | --- |</span>
@@ -573,7 +573,7 @@
 <tbody>
 <tr>
   <td>If $2$ dice are rolled at the same time, the probability of getting a sum of $5 =$</td>
-  <td>$rac{4}{36}$</td>
+  <td>$\frac{4}{36}$</td>
 </tr>
 </tbody>
 </table>
@@ -593,7 +593,7 @@
     </div>
     <a class="headerlink" href="#mean_median"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="mean_median-149"><a href="#mean_median-149"><span class="linenos">149</span></a><span class="k">def</span> <span class="nf">mean_median</span><span class="p">(</span><span class="n">max_length</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
-</span><span id="mean_median-150"><a href="#mean_median-150"><span class="linenos">150</span></a>    <span class="sd">&quot;&quot;&quot;Mean and Median</span>
+</span><span id="mean_median-150"><a href="#mean_median-150"><span class="linenos">150</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Mean and Median</span>
 </span><span id="mean_median-151"><a href="#mean_median-151"><span class="linenos">151</span></a>
 </span><span id="mean_median-152"><a href="#mean_median-152"><span class="linenos">152</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="mean_median-153"><a href="#mean_median-153"><span class="linenos">153</span></a><span class="sd">    | --- | --- |</span>
@@ -645,7 +645,7 @@
     </div>
     <a class="headerlink" href="#permutation"></a>
             <div class="pdoc-code codehilite"><pre><span></span><span id="permutation-169"><a href="#permutation-169"><span class="linenos">169</span></a><span class="k">def</span> <span class="nf">permutation</span><span class="p">(</span><span class="n">max_lengthgth</span><span class="o">=</span><span class="mi">20</span><span class="p">):</span>
-</span><span id="permutation-170"><a href="#permutation-170"><span class="linenos">170</span></a>    <span class="sd">&quot;&quot;&quot;Permutations</span>
+</span><span id="permutation-170"><a href="#permutation-170"><span class="linenos">170</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Permutations</span>
 </span><span id="permutation-171"><a href="#permutation-171"><span class="linenos">171</span></a>
 </span><span id="permutation-172"><a href="#permutation-172"><span class="linenos">172</span></a><span class="sd">    | Ex. Problem | Ex. Solution |</span>
 </span><span id="permutation-173"><a href="#permutation-173"><span class="linenos">173</span></a><span class="sd">    | --- | --- |</span>
@@ -800,7 +800,7 @@
                         if (doc.annotation)
                             heading += `<span class="annotation">${doc.annotation}</span>`;
                         if (doc.default_value)
-                            heading += `<span class="default_value">${doc.default_value}</span>`;
+                            heading += `<span class="default_value"> = ${doc.default_value}</span>`;
                         break;
                     default:
                         heading = `<span class="name">${doc.fullname}</span>`;
diff --git a/docs/search.js b/docs/search.js
index 781e3d6..454db05 100644
--- a/docs/search.js
+++ b/docs/search.js
@@ -1,6 +1,6 @@
 window.pdocSearch = (function(){
 /** elasticlunr - http://weixsong.github.io * Copyright (C) 2017 Oliver Nightingale * Copyright (C) 2017 Wei Song * MIT Licensed */!function(){function e(e){if(null===e||"object"!=typeof e)return e;var t=e.constructor();for(var n in e)e.hasOwnProperty(n)&&(t[n]=e[n]);return t}var t=function(e){var n=new t.Index;return n.pipeline.add(t.trimmer,t.stopWordFilter,t.stemmer),e&&e.call(n,n),n};t.version="0.9.5",lunr=t,t.utils={},t.utils.warn=function(e){return function(t){e.console&&console.warn&&console.warn(t)}}(this),t.utils.toString=function(e){return void 0===e||null===e?"":e.toString()},t.EventEmitter=function(){this.events={}},t.EventEmitter.prototype.addListener=function(){var e=Array.prototype.slice.call(arguments),t=e.pop(),n=e;if("function"!=typeof t)throw new TypeError("last argument must be a function");n.forEach(function(e){this.hasHandler(e)||(this.events[e]=[]),this.events[e].push(t)},this)},t.EventEmitter.prototype.removeListener=function(e,t){if(this.hasHandler(e)){var n=this.events[e].indexOf(t);-1!==n&&(this.events[e].splice(n,1),0==this.events[e].length&&delete this.events[e])}},t.EventEmitter.prototype.emit=function(e){if(this.hasHandler(e)){var t=Array.prototype.slice.call(arguments,1);this.events[e].forEach(function(e){e.apply(void 0,t)},this)}},t.EventEmitter.prototype.hasHandler=function(e){return e in this.events},t.tokenizer=function(e){if(!arguments.length||null===e||void 0===e)return[];if(Array.isArray(e)){var n=e.filter(function(e){return null===e||void 0===e?!1:!0});n=n.map(function(e){return t.utils.toString(e).toLowerCase()});var i=[];return n.forEach(function(e){var n=e.split(t.tokenizer.seperator);i=i.concat(n)},this),i}return e.toString().trim().toLowerCase().split(t.tokenizer.seperator)},t.tokenizer.defaultSeperator=/[\s\-]+/,t.tokenizer.seperator=t.tokenizer.defaultSeperator,t.tokenizer.setSeperator=function(e){null!==e&&void 0!==e&&"object"==typeof e&&(t.tokenizer.seperator=e)},t.tokenizer.resetSeperator=function(){t.tokenizer.seperator=t.tokenizer.defaultSeperator},t.tokenizer.getSeperator=function(){return t.tokenizer.seperator},t.Pipeline=function(){this._queue=[]},t.Pipeline.registeredFunctions={},t.Pipeline.registerFunction=function(e,n){n in t.Pipeline.registeredFunctions&&t.utils.warn("Overwriting existing registered function: "+n),e.label=n,t.Pipeline.registeredFunctions[n]=e},t.Pipeline.getRegisteredFunction=function(e){return e in t.Pipeline.registeredFunctions!=!0?null:t.Pipeline.registeredFunctions[e]},t.Pipeline.warnIfFunctionNotRegistered=function(e){var n=e.label&&e.label in this.registeredFunctions;n||t.utils.warn("Function is not registered with pipeline. This may cause problems when serialising the index.\n",e)},t.Pipeline.load=function(e){var n=new t.Pipeline;return e.forEach(function(e){var i=t.Pipeline.getRegisteredFunction(e);if(!i)throw new Error("Cannot load un-registered function: "+e);n.add(i)}),n},t.Pipeline.prototype.add=function(){var e=Array.prototype.slice.call(arguments);e.forEach(function(e){t.Pipeline.warnIfFunctionNotRegistered(e),this._queue.push(e)},this)},t.Pipeline.prototype.after=function(e,n){t.Pipeline.warnIfFunctionNotRegistered(n);var i=this._queue.indexOf(e);if(-1===i)throw new Error("Cannot find existingFn");this._queue.splice(i+1,0,n)},t.Pipeline.prototype.before=function(e,n){t.Pipeline.warnIfFunctionNotRegistered(n);var i=this._queue.indexOf(e);if(-1===i)throw new Error("Cannot find existingFn");this._queue.splice(i,0,n)},t.Pipeline.prototype.remove=function(e){var t=this._queue.indexOf(e);-1!==t&&this._queue.splice(t,1)},t.Pipeline.prototype.run=function(e){for(var t=[],n=e.length,i=this._queue.length,o=0;n>o;o++){for(var r=e[o],s=0;i>s&&(r=this._queue[s](r,o,e),void 0!==r&&null!==r);s++);void 0!==r&&null!==r&&t.push(r)}return t},t.Pipeline.prototype.reset=function(){this._queue=[]},t.Pipeline.prototype.get=function(){return this._queue},t.Pipeline.prototype.toJSON=function(){return this._queue.map(function(e){return t.Pipeline.warnIfFunctionNotRegistered(e),e.label})},t.Index=function(){this._fields=[],this._ref="id",this.pipeline=new t.Pipeline,this.documentStore=new t.DocumentStore,this.index={},this.eventEmitter=new t.EventEmitter,this._idfCache={},this.on("add","remove","update",function(){this._idfCache={}}.bind(this))},t.Index.prototype.on=function(){var e=Array.prototype.slice.call(arguments);return this.eventEmitter.addListener.apply(this.eventEmitter,e)},t.Index.prototype.off=function(e,t){return this.eventEmitter.removeListener(e,t)},t.Index.load=function(e){e.version!==t.version&&t.utils.warn("version mismatch: current "+t.version+" importing "+e.version);var n=new this;n._fields=e.fields,n._ref=e.ref,n.documentStore=t.DocumentStore.load(e.documentStore),n.pipeline=t.Pipeline.load(e.pipeline),n.index={};for(var i in e.index)n.index[i]=t.InvertedIndex.load(e.index[i]);return n},t.Index.prototype.addField=function(e){return this._fields.push(e),this.index[e]=new t.InvertedIndex,this},t.Index.prototype.setRef=function(e){return this._ref=e,this},t.Index.prototype.saveDocument=function(e){return this.documentStore=new t.DocumentStore(e),this},t.Index.prototype.addDoc=function(e,n){if(e){var n=void 0===n?!0:n,i=e[this._ref];this.documentStore.addDoc(i,e),this._fields.forEach(function(n){var o=this.pipeline.run(t.tokenizer(e[n]));this.documentStore.addFieldLength(i,n,o.length);var r={};o.forEach(function(e){e in r?r[e]+=1:r[e]=1},this);for(var s in r){var u=r[s];u=Math.sqrt(u),this.index[n].addToken(s,{ref:i,tf:u})}},this),n&&this.eventEmitter.emit("add",e,this)}},t.Index.prototype.removeDocByRef=function(e){if(e&&this.documentStore.isDocStored()!==!1&&this.documentStore.hasDoc(e)){var t=this.documentStore.getDoc(e);this.removeDoc(t,!1)}},t.Index.prototype.removeDoc=function(e,n){if(e){var n=void 0===n?!0:n,i=e[this._ref];this.documentStore.hasDoc(i)&&(this.documentStore.removeDoc(i),this._fields.forEach(function(n){var o=this.pipeline.run(t.tokenizer(e[n]));o.forEach(function(e){this.index[n].removeToken(e,i)},this)},this),n&&this.eventEmitter.emit("remove",e,this))}},t.Index.prototype.updateDoc=function(e,t){var t=void 0===t?!0:t;this.removeDocByRef(e[this._ref],!1),this.addDoc(e,!1),t&&this.eventEmitter.emit("update",e,this)},t.Index.prototype.idf=function(e,t){var n="@"+t+"/"+e;if(Object.prototype.hasOwnProperty.call(this._idfCache,n))return this._idfCache[n];var i=this.index[t].getDocFreq(e),o=1+Math.log(this.documentStore.length/(i+1));return this._idfCache[n]=o,o},t.Index.prototype.getFields=function(){return this._fields.slice()},t.Index.prototype.search=function(e,n){if(!e)return[];e="string"==typeof e?{any:e}:JSON.parse(JSON.stringify(e));var i=null;null!=n&&(i=JSON.stringify(n));for(var o=new t.Configuration(i,this.getFields()).get(),r={},s=Object.keys(e),u=0;u<s.length;u++){var a=s[u];r[a]=this.pipeline.run(t.tokenizer(e[a]))}var l={};for(var c in o){var d=r[c]||r.any;if(d){var f=this.fieldSearch(d,c,o),h=o[c].boost;for(var p in f)f[p]=f[p]*h;for(var p in f)p in l?l[p]+=f[p]:l[p]=f[p]}}var v,g=[];for(var p in l)v={ref:p,score:l[p]},this.documentStore.hasDoc(p)&&(v.doc=this.documentStore.getDoc(p)),g.push(v);return g.sort(function(e,t){return t.score-e.score}),g},t.Index.prototype.fieldSearch=function(e,t,n){var i=n[t].bool,o=n[t].expand,r=n[t].boost,s=null,u={};return 0!==r?(e.forEach(function(e){var 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-    /** pdoc search index */const docs = {"version": "0.9.5", "fields": ["qualname", "fullname", "annotation", "default_value", "signature", "bases", "doc"], "ref": "fullname", "documentStore": {"docs": {"mathgenerator": {"fullname": "mathgenerator", "modulename": "mathgenerator", "kind": "module", "doc": "<h1 id=\"mathgenerator\">mathgenerator</h1>\n\n<p>A math problem generator, created for the purpose of giving teachers and students the means to easily get access to random math exercises to suit their needs.</p>\n\n<p>To try out generators, go to <a href=\"https://mathgenerator-demo.netlify.app\">https://mathgenerator-demo.netlify.app</a></p>\n\n<p>See <a href=\"https://github.com/lukew3/mathgenerator/blob/main/CONTRIBUTING.md\">CONTRIBUTING.md</a> for information about how to contribute.</p>\n\n<h2 id=\"table-of-contents\">Table of Contents</h2>\n\n<ul>\n<li><a href=\"#installation\">Installation</a></li>\n<li><a href=\"#usage\">Usage</a></li>\n<li><a href=\"#documentation\">Documentation</a></li>\n</ul>\n\n<h2 id=\"installation\">Installation</h2>\n\n<p>The project can be install via pip</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code>pip install mathgenerator\n</code></pre>\n</div>\n\n<h2 id=\"usage\">Usage</h2>\n\n<p>Here is an example of how you would generate an addition problem:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span> <span class=\"nn\">mathgenerator</span>\n\n<span class=\"c1\">#generate an addition problem</span>\n<span class=\"n\">problem</span><span class=\"p\">,</span> <span class=\"n\">solution</span> <span class=\"o\">=</span> <span class=\"n\">mathgenerator</span><span class=\"o\">.</span><span class=\"n\">addition</span><span class=\"p\">()</span>\n\n<span class=\"c1\">#another way to generate an addition problem using genById()</span>\n<span class=\"n\">problem</span><span class=\"p\">,</span> <span class=\"n\">solution</span> <span class=\"o\">=</span> <span class=\"n\">mathgenerator</span><span class=\"o\">.</span><span class=\"n\">genById</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>You may prefer to use <code>import mathgenerator as mg</code> and run functions like <code>mg.addition()</code> so that you don't have to type as much.\n<!--</p>\n\n<h3 id=\"creating-a-worksheet\">Creating a worksheet</h3>\n\n<p>If you wish to create a worksheet, you can use the <a href=\"https://github.com/lukew3/worksheetgen\">worksheetgen</a> package. Install this with <code>pip install worksheetgen</code>. Here is an example of how a worksheet would be generated.</p>\n\n<pre><code>from mathgenerator import mathgen\nfrom worksheetgen.wg import Worksheet\n\nws = Worksheet(\"Worksheet title\")\nwith ws.section('Section 1', description='These are instructions')\n    # Writes 10 problems generated with id 1, [0] at the end specifies to take problem, and not solution.\n    for _ in range(10):\n        ws.add_problem(mathgen.genById(1)[0])\nws.write_pdf()\n</code></pre>\n\n<p>This creates the pdf <code>ws.pdf</code> in your current directory\n-->\nProblem/solution pairs are generated with either:</p>\n\n<ul>\n<li><code>mathgenerator.&lt;generator_name&gt;()</code> - generates a problem, solution set from the given generator name.</li>\n<li><code>mathgenerator.genById(id)</code> - generates a problem, solution set with generator id provided by the <code>id</code> parameter</li>\n</ul>\n\n<p><!--</p>\n\n<h4 id=\"format-kwarg\"><code>format</code> kwarg</h4>\n\n<ul>\n<li>Pass <code>format=latex</code> to return problem and solution set as latex. If latex is not available for that generator, the problem will return the string \"Latex unavailable\"</li>\n<li>Pass <code>format=raw</code> to return just the raw data for each generator. An array of each variable necessary to the generator is returned.</li>\n<li>If you don't pass a value to the format kwarg, the generator will return a problem and answer in asciimath format.\n-->\nYou can also use <code>getGenList()</code> to return a list of all generators included in the library in the format:</li>\n</ul>\n\n<pre><code>[funcname, subjectname]\n</code></pre>\n\n<h2 id=\"documentation\">Documentation</h2>\n\n<p>Documentation can be found at <a href=\"https://lukew3.github.io/mathgenerator\">https://lukew3.github.io/mathgenerator</a></p>\n"}, "mathgenerator.get_gen_list": {"fullname": "mathgenerator.get_gen_list", "modulename": "mathgenerator", "qualname": "get_gen_list", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.gen_by_id": {"fullname": "mathgenerator.gen_by_id", "modulename": "mathgenerator", "qualname": "gen_by_id", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"nb\">id</span>, </span><span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.getGenList": {"fullname": "mathgenerator.getGenList", "modulename": "mathgenerator", "qualname": "getGenList", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.genById": {"fullname": "mathgenerator.genById", "modulename": "mathgenerator", "qualname": "genById", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"nb\">id</span>, </span><span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.algebra": {"fullname": "mathgenerator.algebra", "modulename": "mathgenerator.algebra", "kind": "module", "doc": "<p></p>\n"}, "mathgenerator.algebra.basic_algebra": {"fullname": "mathgenerator.algebra.basic_algebra", "modulename": "mathgenerator.algebra", "qualname": "basic_algebra", "kind": "function", "doc": "<p>Basic Algebra</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$1x + 5 = 5$</td>\n  <td>$0$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_variable</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.algebra.combine_like_terms": {"fullname": "mathgenerator.algebra.combine_like_terms", "modulename": "mathgenerator.algebra", "qualname": "combine_like_terms", "kind": "function", "doc": "<p>Combine Like Terms</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$6x^{9} + 3x^{2} + 5x^{19} + 3x^{17}$</td>\n  <td>$3x^{2} + 6x^{9} + 3x^{17} + 5x^{19}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_coef</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">max_exp</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_terms</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.algebra.complex_quadratic": {"fullname": "mathgenerator.algebra.complex_quadratic", "modulename": "mathgenerator.algebra", "qualname": "complex_quadratic", "kind": "function", "doc": "<p>Complex Quadratic Equation</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Find the roots of given Quadratic Equation $x^2 + 8x + 8 = 0$</td>\n  <td>$((-1.172, -6.828)) = (\\frac{-8 + \\sqrt{32}}{2<em>1}, (\\frac{-8 - \\sqrt{32}}{2</em>1})$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">prob_type</span><span class=\"o\">=</span><span class=\"mi\">0</span>, </span><span class=\"param\"><span class=\"n\">max_range</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.algebra.compound_interest": {"fullname": "mathgenerator.algebra.compound_interest", "modulename": "mathgenerator.algebra", "qualname": "compound_interest", "kind": "function", "doc": "<p>Compound Interest</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Compound interest for a principle amount of $2679$ dollars, $9$% rate of interest and for a time period of $3$ years is $=$</td>\n  <td>$3469.38$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_principle</span><span class=\"o\">=</span><span class=\"mi\">10000</span>, </span><span class=\"param\"><span class=\"n\">max_rate</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">max_time</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.algebra.distance_two_points": {"fullname": "mathgenerator.algebra.distance_two_points", "modulename": "mathgenerator.algebra", "qualname": "distance_two_points", "kind": "function", "doc": "<p>Distance between 2 points</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Find the distance between $(-19, -6)$ and $(15, -16)$</td>\n  <td>$\\sqrt{1256}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_val_xy</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">min_val_xy</span><span class=\"o\">=-</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.algebra.expanding": {"fullname": "mathgenerator.algebra.expanding", "modulename": "mathgenerator.algebra", "qualname": "expanding", "kind": "function", "doc": "<p>Expanding Factored Binomial</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$(x-6)(-3x-3)$</td>\n  <td>$x^2+18x+18$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">range_x1</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">range_x2</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">range_a</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">range_b</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.algebra.factoring": {"fullname": "mathgenerator.algebra.factoring", "modulename": "mathgenerator.algebra", "qualname": "factoring", "kind": "function", "doc": "<p>Factoring Quadratic\nGiven a quadratic equation in the form x^2 + bx + c, factor it into it's roots (x - x1)(x -x2)</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$x^2+2x-24$</td>\n  <td>$(x-4)(x+6)$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">range_x1</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">range_x2</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.algebra.int_matrix_22_determinant": {"fullname": "mathgenerator.algebra.int_matrix_22_determinant", "modulename": "mathgenerator.algebra", "qualname": "int_matrix_22_determinant", "kind": "function", "doc": "<p>Determinant to 2x2 Matrix</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$\\det \\begin{bmatrix} 88 &amp; 40 \\\\ 9 &amp; 91 \\end{bmatrix}= $</td>\n  <td>$7648$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_matrix_val</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.algebra.intersection_of_two_lines": {"fullname": "mathgenerator.algebra.intersection_of_two_lines", "modulename": "mathgenerator.algebra", "qualname": "intersection_of_two_lines", "kind": "function", "doc": "<p>Intersection of two lines</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Find the point of intersection of the two lines: $y = \\frac{-2}{6}x + 3$ and $y = \\frac{3}{6}x - 8$</td>\n  <td>$(\\frac{66}{5}, \\frac{-7}{5})$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">min_m</span><span class=\"o\">=-</span><span class=\"mi\">10</span>,</span><span class=\"param\">\t<span class=\"n\">max_m</span><span class=\"o\">=</span><span class=\"mi\">10</span>,</span><span class=\"param\">\t<span class=\"n\">min_b</span><span class=\"o\">=-</span><span class=\"mi\">10</span>,</span><span class=\"param\">\t<span class=\"n\">max_b</span><span class=\"o\">=</span><span class=\"mi\">10</span>,</span><span class=\"param\">\t<span class=\"n\">min_denominator</span><span class=\"o\">=</span><span class=\"mi\">1</span>,</span><span class=\"param\">\t<span class=\"n\">max_denominator</span><span class=\"o\">=</span><span class=\"mi\">6</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.algebra.invert_matrix": {"fullname": "mathgenerator.algebra.invert_matrix", "modulename": "mathgenerator.algebra", "qualname": "invert_matrix", "kind": "function", "doc": "<p>Invert Matrix</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Inverse of Matrix $\\begin{bmatrix} 4 &amp; 1 &amp; 4 \\\\ 5 &amp; 1 &amp; 5 \\\\ 12 &amp; 3 &amp; 13 \\end{bmatrix}$ is:</td>\n  <td>$\\begin{bmatrix} 2 &amp; 1 &amp; -1 \\\\ 5 &amp; -4 &amp; 0 \\\\ -3 &amp; 0 &amp; 1 \\end{bmatrix}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">square_matrix_dimension</span><span class=\"o\">=</span><span class=\"mi\">3</span>,</span><span class=\"param\">\t<span class=\"n\">max_matrix_element</span><span class=\"o\">=</span><span class=\"mi\">99</span>,</span><span class=\"param\">\t<span class=\"n\">only_integer_elements_in_inverted_matrixe</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.algebra.linear_equations": {"fullname": "mathgenerator.algebra.linear_equations", "modulename": "mathgenerator.algebra", "qualname": "linear_equations", "kind": "function", "doc": "<p>Linear Equations</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Given the equations $10x + -20y = 310$ and $-16x + -17y = 141$, solve for $x$ and $y$</td>\n  <td>$x = 5$, $y = -13$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">n</span><span class=\"o\">=</span><span class=\"mi\">2</span>, </span><span class=\"param\"><span class=\"n\">var_range</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">coeff_range</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.algebra.line_equation_from_2_points": {"fullname": "mathgenerator.algebra.line_equation_from_2_points", "modulename": "mathgenerator.algebra", "qualname": "line_equation_from_2_points", "kind": "function", "doc": "<p>Equation of Line from Two Points</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Find the equation of the line passing through the points $(-19,-8)$ and $(-2,0)$.</td>\n  <td>$y=\\frac{8}{17}x+\\frac{16}{17}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.algebra.log": {"fullname": "mathgenerator.algebra.log", "modulename": "mathgenerator.algebra", "qualname": "log", "kind": "function", "doc": "<p>Logarithm</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$log_{3}(243)=$</td>\n  <td>$5$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_base</span><span class=\"o\">=</span><span class=\"mi\">3</span>, </span><span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">8</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.algebra.matrix_multiplication": {"fullname": "mathgenerator.algebra.matrix_multiplication", "modulename": "mathgenerator.algebra", "qualname": "matrix_multiplication", "kind": "function", "doc": "<p>Multiply Two Matrices</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Multiply $\\begin{bmatrix} 15 &amp; 72 \\\\ 64 &amp; -20 \\\\ 18 &amp; 59 \\\\ -21 &amp; -55 \\\\ 20 &amp; -12 \\\\ -75 &amp; -42 \\\\ 47 &amp; 89 \\\\ -53 &amp; 27 \\\\ -56 &amp; 44 \\end{bmatrix}$ and $\\begin{bmatrix} 49 &amp; -2 &amp; 68 &amp; -28 \\\\ 49 &amp; 6 &amp; 83 &amp; 42 \\end{bmatrix}$</td>\n  <td>$\\begin{bmatrix} 4263 &amp; 402 &amp; 6996 &amp; 2604 \\\\ 2156 &amp; -248 &amp; 2692 &amp; -2632 \\\\ 3773 &amp; 318 &amp; 6121 &amp; 1974 \\\\ -3724 &amp; -288 &amp; -5993 &amp; -1722 \\\\ 392 &amp; -112 &amp; 364 &amp; -1064 \\\\ -5733 &amp; -102 &amp; -8586 &amp; 336 \\\\ 6664 &amp; 440 &amp; 10583 &amp; 2422 \\\\ -1274 &amp; 268 &amp; -1363 &amp; 2618 \\\\ -588 &amp; 376 &amp; -156 &amp; 3416 \\end{bmatrix}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">100</span>, </span><span class=\"param\"><span class=\"n\">max_dim</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.algebra.midpoint_of_two_points": {"fullname": "mathgenerator.algebra.midpoint_of_two_points", "modulename": "mathgenerator.algebra", "qualname": "midpoint_of_two_points", "kind": "function", "doc": "<p>Midpoint of two points</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>The midpoint of $(-8,10)$ and $(18,0) = $</td>\n  <td>$(5.0,5.0)$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_value</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.algebra.multiply_complex_numbers": {"fullname": "mathgenerator.algebra.multiply_complex_numbers", "modulename": "mathgenerator.algebra", "qualname": "multiply_complex_numbers", "kind": "function", "doc": "<p>Multiplication of 2 complex numbers</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$(14+18j) * (14+15j) = $</td>\n  <td>$(-74+462j)$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">min_real_imaginary_num</span><span class=\"o\">=-</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_real_imaginary_num</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.algebra.multiply_int_to_22_matrix": {"fullname": "mathgenerator.algebra.multiply_int_to_22_matrix", "modulename": "mathgenerator.algebra", "qualname": "multiply_int_to_22_matrix", "kind": "function", "doc": "<p>Multiply Integer to 2x2 Matrix</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$5 * \\begin{bmatrix} 1 &amp; 0 \\\\ 2 &amp; 9 \\end{bmatrix} =$</td>\n  <td>$\\begin{bmatrix} 5 &amp; 0 \\\\ 10 &amp; 45 \\end{bmatrix}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_matrix_val</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">max_res</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.algebra.quadratic_equation": {"fullname": "mathgenerator.algebra.quadratic_equation", "modulename": "mathgenerator.algebra", "qualname": "quadratic_equation", "kind": "function", "doc": "<p>Quadratic Equation</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>What are the zeros of the quadratic equation $22x^2+137x+25=0$</td>\n  <td>${-0.19, -6.04}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.algebra.simple_interest": {"fullname": "mathgenerator.algebra.simple_interest", "modulename": "mathgenerator.algebra", "qualname": "simple_interest", "kind": "function", "doc": "<p>Simple Interest</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Simple interest for a principle amount of $7217$ dollars, $3$% rate of interest and for a time period of $10$ years is $=$</td>\n  <td>$2165.1$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_principle</span><span class=\"o\">=</span><span class=\"mi\">10000</span>, </span><span class=\"param\"><span class=\"n\">max_rate</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">max_time</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.algebra.system_of_equations": {"fullname": "mathgenerator.algebra.system_of_equations", "modulename": "mathgenerator.algebra", "qualname": "system_of_equations", "kind": "function", "doc": "<p>Solve a System of Equations in R^2</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Given $-x + 5y = -28$ and $9x + 2y = 64$, solve for $x$ and $y$.</td>\n  <td>$x = 8$, $y = -4$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">range_x</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">range_y</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">coeff_mult_range</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.algebra.vector_cross": {"fullname": "mathgenerator.algebra.vector_cross", "modulename": "mathgenerator.algebra", "qualname": "vector_cross", "kind": "function", "doc": "<p>Cross product of 2 vectors</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$[-1, -4, 10] \\times [-11, 1, -16] = $</td>\n  <td>$[54, -126, -45]$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">min_val</span><span class=\"o\">=-</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.algebra.vector_dot": {"fullname": "mathgenerator.algebra.vector_dot", "modulename": "mathgenerator.algebra", "qualname": "vector_dot", "kind": "function", "doc": "<p>Dot product of 2 vectors</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$[12, -9, -8]\\cdot[-9, 8, 1]=$</td>\n  <td>$-188$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">min_val</span><span class=\"o\">=-</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.basic_math": {"fullname": "mathgenerator.basic_math", "modulename": "mathgenerator.basic_math", "kind": "module", "doc": "<p></p>\n"}, "mathgenerator.basic_math.absolute_difference": {"fullname": "mathgenerator.basic_math.absolute_difference", "modulename": "mathgenerator.basic_math", "qualname": "absolute_difference", "kind": "function", "doc": "<p>Absolute difference between two numbers</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$</td>\n  <td>22-34</td>\n  <td>=$</td>\n  <td>$12$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_a</span><span class=\"o\">=</span><span class=\"mi\">100</span>, </span><span class=\"param\"><span class=\"n\">max_b</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.basic_math.addition": {"fullname": "mathgenerator.basic_math.addition", "modulename": "mathgenerator.basic_math", "qualname": "addition", "kind": "function", "doc": "<p>Addition of two numbers</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$22+34=$</td>\n  <td>$56$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_sum</span><span class=\"o\">=</span><span class=\"mi\">99</span>, </span><span class=\"param\"><span class=\"n\">max_addend</span><span class=\"o\">=</span><span class=\"mi\">50</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.basic_math.compare_fractions": {"fullname": "mathgenerator.basic_math.compare_fractions", "modulename": "mathgenerator.basic_math", "qualname": "compare_fractions", "kind": "function", "doc": "<p>Compare Fractions</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Which symbol represents the comparison between $\\frac{1}{2}$ and $\\frac{3}{4}$?</td>\n  <td>$&gt;$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.basic_math.cube_root": {"fullname": "mathgenerator.basic_math.cube_root", "modulename": "mathgenerator.basic_math", "qualname": "cube_root", "kind": "function", "doc": "<p>Cube Root</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>What is the cube root of: $\\sqrt[3]{125}=$ to 2 decimal places?</td>\n  <td>$5$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">min_no</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">max_no</span><span class=\"o\">=</span><span class=\"mi\">1000</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.basic_math.divide_fractions": {"fullname": "mathgenerator.basic_math.divide_fractions", "modulename": "mathgenerator.basic_math", "qualname": "divide_fractions", "kind": "function", "doc": "<p>Divide Fractions</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$\\frac{7}{9}\\div\\frac{4}{1}=$</td>\n  <td>$\\frac{7}{36}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.basic_math.division": {"fullname": "mathgenerator.basic_math.division", "modulename": "mathgenerator.basic_math", "qualname": "division", "kind": "function", "doc": "<p>Division</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$216\\div24=$</td>\n  <td>$9$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_a</span><span class=\"o\">=</span><span class=\"mi\">25</span>, </span><span class=\"param\"><span class=\"n\">max_b</span><span class=\"o\">=</span><span class=\"mi\">25</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.basic_math.exponentiation": {"fullname": "mathgenerator.basic_math.exponentiation", "modulename": "mathgenerator.basic_math", "qualname": "exponentiation", "kind": "function", "doc": "<p>Exponentiation</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$9^{5}=$</td>\n  <td>$8$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_base</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_expo</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.basic_math.factorial": {"fullname": "mathgenerator.basic_math.factorial", "modulename": "mathgenerator.basic_math", "qualname": "factorial", "kind": "function", "doc": "<p>Factorial</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$4! =$</td>\n  <td>$24$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_input</span><span class=\"o\">=</span><span class=\"mi\">6</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.basic_math.fraction_multiplication": {"fullname": "mathgenerator.basic_math.fraction_multiplication", "modulename": "mathgenerator.basic_math", "qualname": "fraction_multiplication", "kind": "function", "doc": "<p>Fraction Multiplication</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$\\frac{3}{10}\\cdot\\frac{6}{7}=$</td>\n  <td>$\\frac{9}{35}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.basic_math.fraction_to_decimal": {"fullname": "mathgenerator.basic_math.fraction_to_decimal", "modulename": "mathgenerator.basic_math", "qualname": "fraction_to_decimal", "kind": "function", "doc": "<p>Fraction to Decimal</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$83\\div80=$</td>\n  <td>$1.04$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_res</span><span class=\"o\">=</span><span class=\"mi\">99</span>, </span><span class=\"param\"><span class=\"n\">max_divid</span><span class=\"o\">=</span><span class=\"mi\">99</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.basic_math.greatest_common_divisor": {"fullname": "mathgenerator.basic_math.greatest_common_divisor", "modulename": "mathgenerator.basic_math", "qualname": "greatest_common_divisor", "kind": "function", "doc": "<p>Greatest Common Divisor of N Numbers ( GCD / HCF )</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$GCD(488075608, 75348096)=$</td>\n  <td>$8$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">numbers_count</span><span class=\"o\">=</span><span class=\"mi\">2</span>, </span><span class=\"param\"><span class=\"n\">max_num</span><span class=\"o\">=</span><span class=\"mi\">1000</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.basic_math.is_composite": {"fullname": "mathgenerator.basic_math.is_composite", "modulename": "mathgenerator.basic_math", "qualname": "is_composite", "kind": "function", "doc": "<p>Is Composite</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Is $171$ composite?</td>\n  <td>Yes</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_num</span><span class=\"o\">=</span><span class=\"mi\">250</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.basic_math.is_prime": {"fullname": "mathgenerator.basic_math.is_prime", "modulename": "mathgenerator.basic_math", "qualname": "is_prime", "kind": "function", "doc": "<p>Is Prime</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Is $37$ prime?</td>\n  <td>Yes</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_num</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.basic_math.multiplication": {"fullname": "mathgenerator.basic_math.multiplication", "modulename": "mathgenerator.basic_math", "qualname": "multiplication", "kind": "function", "doc": "<p>Multiplication</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$10\\cdot9=$</td>\n  <td>$90$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_multi</span><span class=\"o\">=</span><span class=\"mi\">12</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.basic_math.percentage": {"fullname": "mathgenerator.basic_math.percentage", "modulename": "mathgenerator.basic_math", "qualname": "percentage", "kind": "function", "doc": "<p>Percentage of a number</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>What is $45$% of $39$?</td>\n  <td>$17.55$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_value</span><span class=\"o\">=</span><span class=\"mi\">99</span>, </span><span class=\"param\"><span class=\"n\">max_percentage</span><span class=\"o\">=</span><span class=\"mi\">99</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.basic_math.percentage_difference": {"fullname": "mathgenerator.basic_math.percentage_difference", "modulename": "mathgenerator.basic_math", "qualname": "percentage_difference", "kind": "function", "doc": "<p>Percentage difference between two numbers</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>What is the percentage difference between $2$ and $10$?</td>\n  <td>$133.33$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_value</span><span class=\"o\">=</span><span class=\"mi\">200</span>, </span><span class=\"param\"><span class=\"n\">min_value</span><span class=\"o\">=</span><span class=\"mi\">0</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.basic_math.percentage_error": {"fullname": "mathgenerator.basic_math.percentage_error", "modulename": "mathgenerator.basic_math", "qualname": "percentage_error", "kind": "function", "doc": "<p>Percentage error</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Find the percentage error when observed value equals $32$ and exact value equals $81$.</td>\n  <td>$60.49$%</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_value</span><span class=\"o\">=</span><span class=\"mi\">100</span>, </span><span class=\"param\"><span class=\"n\">min_value</span><span class=\"o\">=-</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.basic_math.power_of_powers": {"fullname": "mathgenerator.basic_math.power_of_powers", "modulename": "mathgenerator.basic_math", "qualname": "power_of_powers", "kind": "function", "doc": "<p>Power of Powers</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Simplify $18^{10^{8}}$</td>\n  <td>$18^{80}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_base</span><span class=\"o\">=</span><span class=\"mi\">50</span>, </span><span class=\"param\"><span class=\"n\">max_power</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.basic_math.square": {"fullname": "mathgenerator.basic_math.square", "modulename": "mathgenerator.basic_math", "qualname": "square", "kind": "function", "doc": "<p>Square</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$17^2=$</td>\n  <td>$289$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_square_num</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.basic_math.square_root": {"fullname": "mathgenerator.basic_math.square_root", "modulename": "mathgenerator.basic_math", "qualname": "square_root", "kind": "function", "doc": "<p>Square Root</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$\\sqrt{64}=$</td>\n  <td>$8$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">min_no</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">max_no</span><span class=\"o\">=</span><span class=\"mi\">12</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.basic_math.simplify_square_root": {"fullname": "mathgenerator.basic_math.simplify_square_root", "modulename": "mathgenerator.basic_math", "qualname": "simplify_square_root", "kind": "function", "doc": "<p>Simplify Square Root</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$\\sqrt{63}$</td>\n  <td>$3\\sqrt{7}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_variable</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.basic_math.subtraction": {"fullname": "mathgenerator.basic_math.subtraction", "modulename": "mathgenerator.basic_math", "qualname": "subtraction", "kind": "function", "doc": "<p>Subtraction of two numbers</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$54-22=$</td>\n  <td>$32$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_minuend</span><span class=\"o\">=</span><span class=\"mi\">99</span>, </span><span class=\"param\"><span class=\"n\">max_diff</span><span class=\"o\">=</span><span class=\"mi\">99</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.calculus": {"fullname": "mathgenerator.calculus", "modulename": "mathgenerator.calculus", "kind": "module", "doc": "<p></p>\n"}, "mathgenerator.calculus.definite_integral": {"fullname": "mathgenerator.calculus.definite_integral", "modulename": "mathgenerator.calculus", "qualname": "definite_integral", "kind": "function", "doc": "<p>Definite Integral of Quadratic Equation</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>The definite integral within limits $0$ to $1$ of the equation $28x^2 + 32x + 66 = $</td>\n  <td>$91.33$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_coef</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.calculus.power_rule_differentiation": {"fullname": "mathgenerator.calculus.power_rule_differentiation", "modulename": "mathgenerator.calculus", "qualname": "power_rule_differentiation", "kind": "function", "doc": "<p>Power Rule Differentiation</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Differentiate $1x^{5} + 4x^{7} + 4x^{4}$</td>\n  <td>$5x^{4} + 28x^{6} + 16x^{3}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_coef</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">max_exp</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">max_terms</span><span class=\"o\">=</span><span class=\"mi\">5</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.calculus.power_rule_integration": {"fullname": "mathgenerator.calculus.power_rule_integration", "modulename": "mathgenerator.calculus", "qualname": "power_rule_integration", "kind": "function", "doc": "<p>Power Rule Integration</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Integrate $9x^{6} + 2x^{6} + 4x^{3}$</td>\n  <td>$\\frac{9}{6}x^{7} + \\frac{2}{6}x^{7} + \\frac{4}{3}x^{4} + C$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_coef</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">max_exp</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">max_terms</span><span class=\"o\">=</span><span class=\"mi\">5</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.calculus.stationary_points": {"fullname": "mathgenerator.calculus.stationary_points", "modulename": "mathgenerator.calculus", "qualname": "stationary_points", "kind": "function", "doc": "<p>Stationary Points</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$f(x)=6<em>x^3 + 6</em>x^2 + x + 8$</td>\n  <td>${- \\frac{1}{3} - \\frac{\\sqrt{2}}{6}, - \\frac{1}{3} + \\frac{\\sqrt{2}}{6}}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_exp</span><span class=\"o\">=</span><span class=\"mi\">3</span>, </span><span class=\"param\"><span class=\"n\">max_coef</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.calculus.trig_differentiation": {"fullname": "mathgenerator.calculus.trig_differentiation", "modulename": "mathgenerator.calculus", "qualname": "trig_differentiation", "kind": "function", "doc": "<p>Trigonometric Differentiation</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$\\frac{d}{dx}(\\csc)=$</td>\n  <td>$-\\csc \\cdot \\cot$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.computer_science": {"fullname": "mathgenerator.computer_science", "modulename": "mathgenerator.computer_science", "kind": "module", "doc": "<p></p>\n"}, "mathgenerator.computer_science.bcd_to_decimal": {"fullname": "mathgenerator.computer_science.bcd_to_decimal", "modulename": "mathgenerator.computer_science", "qualname": "bcd_to_decimal", "kind": "function", "doc": "<p>Binary Coded Decimal to Integer</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Integer of Binary Coded Decimal $4 =$</td>\n  <td>$17801$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_number</span><span class=\"o\">=</span><span class=\"mi\">10000</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.computer_science.binary_2s_complement": {"fullname": "mathgenerator.computer_science.binary_2s_complement", "modulename": "mathgenerator.computer_science", "qualname": "binary_2s_complement", "kind": "function", "doc": "<p>Binary 2's Complement</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>2's complement of $1011 = $</td>\n  <td>$101$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">maxDigits</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.computer_science.binary_complement_1s": {"fullname": "mathgenerator.computer_science.binary_complement_1s", "modulename": "mathgenerator.computer_science", "qualname": "binary_complement_1s", "kind": "function", "doc": "<p>Binary Complement 1s</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$1111001 = $</td>\n  <td>$0000110$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">maxDigits</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.computer_science.binary_to_decimal": {"fullname": "mathgenerator.computer_science.binary_to_decimal", "modulename": "mathgenerator.computer_science", "qualname": "binary_to_decimal", "kind": "function", "doc": "<p>Binary to Decimal</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$000110$</td>\n  <td>$6$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_dig</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.computer_science.binary_to_hex": {"fullname": "mathgenerator.computer_science.binary_to_hex", "modulename": "mathgenerator.computer_science", "qualname": "binary_to_hex", "kind": "function", "doc": "<p>Binary to Hexidecimal</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$010101$</td>\n  <td>$0x15$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_dig</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.computer_science.decimal_to_bcd": {"fullname": "mathgenerator.computer_science.decimal_to_bcd", "modulename": "mathgenerator.computer_science", "qualname": "decimal_to_bcd", "kind": "function", "doc": "<p>Decimal to Binary Coded Decimal</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>BCD of Decimal Number $6575 = $</td>\n  <td>$191015$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_number</span><span class=\"o\">=</span><span class=\"mi\">10000</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.computer_science.decimal_to_binary": {"fullname": "mathgenerator.computer_science.decimal_to_binary", "modulename": "mathgenerator.computer_science", "qualname": "decimal_to_binary", "kind": "function", "doc": "<p>Decimal to Binary</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Binary of $4 = $</td>\n  <td>$100$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_dec</span><span class=\"o\">=</span><span class=\"mi\">99</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.computer_science.decimal_to_hexadeci": {"fullname": "mathgenerator.computer_science.decimal_to_hexadeci", "modulename": "mathgenerator.computer_science", "qualname": "decimal_to_hexadeci", "kind": "function", "doc": "<p>Decimal to Hexadecimal</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Hexadecimal of $410 = $</td>\n  <td>$0x19a$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_dec</span><span class=\"o\">=</span><span class=\"mi\">1000</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.computer_science.decimal_to_octal": {"fullname": "mathgenerator.computer_science.decimal_to_octal", "modulename": "mathgenerator.computer_science", "qualname": "decimal_to_octal", "kind": "function", "doc": "<p>Decimal to Octal</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>The decimal number $3698$ in octal is:</td>\n  <td>$0o7162$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_decimal</span><span class=\"o\">=</span><span class=\"mi\">4096</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.computer_science.fibonacci_series": {"fullname": "mathgenerator.computer_science.fibonacci_series", "modulename": "mathgenerator.computer_science", "qualname": "fibonacci_series", "kind": "function", "doc": "<p>Fibonacci Series</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>The Fibonacci Series of the first ${n}$ numbers is ?</td>\n  <td>$0, 1, 1, 2, 3, 5, 8, 13, 21$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">min_no</span><span class=\"o\">=</span><span class=\"mi\">1</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.computer_science.modulo_division": {"fullname": "mathgenerator.computer_science.modulo_division", "modulename": "mathgenerator.computer_science", "qualname": "modulo_division", "kind": "function", "doc": "<p>Modulo Division</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$43$ % $33 = $</td>\n  <td>$10$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_res</span><span class=\"o\">=</span><span class=\"mi\">99</span>, </span><span class=\"param\"><span class=\"n\">max_modulo</span><span class=\"o\">=</span><span class=\"mi\">99</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.computer_science.nth_fibonacci_number": {"fullname": "mathgenerator.computer_science.nth_fibonacci_number", "modulename": "mathgenerator.computer_science", "qualname": "nth_fibonacci_number", "kind": "function", "doc": "<p>nth Fibonacci number</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>What is the 85th Fibonacci number?</td>\n  <td>$259695496911123328$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_n</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry": {"fullname": "mathgenerator.geometry", "modulename": "mathgenerator.geometry", "kind": "module", "doc": "<p></p>\n"}, "mathgenerator.geometry.angle_btw_vectors": {"fullname": "mathgenerator.geometry.angle_btw_vectors", "modulename": "mathgenerator.geometry", "qualname": "angle_btw_vectors", "kind": "function", "doc": "<p>Angle between 2 vectors</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>angle between the vectors $[363.84, 195.54, 997.08, 39.26, 60.14, 722.7, 888.57, 713.15, 436.22, 712.23, 349.23, 595.91, 191.8, 824.58, 861.56, 122.73, 815.14, 700.68, 506.5]$ and $[760.85, 934.67, 513.37, 796.93, 809.97, 423.54, 162.69, 758.96, 133.42, 478.14, 771.84, 824.88, 483.07, 134.41, 954.41, 893.42, 191.01, 453.97, 648.59]$ is:</td>\n  <td>$0.81$ radians</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_elt_amt</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.angle_regular_polygon": {"fullname": "mathgenerator.geometry.angle_regular_polygon", "modulename": "mathgenerator.geometry", "qualname": "angle_regular_polygon", "kind": "function", "doc": "<p>Angle of a Regular Polygon</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Find the angle of a regular polygon with $8$ sides</td>\n  <td>$135.0$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">min_val</span><span class=\"o\">=</span><span class=\"mi\">3</span>, </span><span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.arc_length": {"fullname": "mathgenerator.geometry.arc_length", "modulename": "mathgenerator.geometry", "qualname": "arc_length", "kind": "function", "doc": "<p>Arc length of Angle</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Given radius, $44$ and angle, $184$. Find the arc length of the angle.</td>\n  <td>Arc length of the angle $= 141.30186$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">49</span>, </span><span class=\"param\"><span class=\"n\">max_angle</span><span class=\"o\">=</span><span class=\"mi\">359</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.area_of_circle": {"fullname": "mathgenerator.geometry.area_of_circle", "modulename": "mathgenerator.geometry", "qualname": "area_of_circle", "kind": "function", "doc": "<p>Area of Circle</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Area of circle with radius $29=$</td>\n  <td>$2642.08$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.area_of_circle_given_center_and_point": {"fullname": "mathgenerator.geometry.area_of_circle_given_center_and_point", "modulename": "mathgenerator.geometry", "qualname": "area_of_circle_given_center_and_point", "kind": "function", "doc": "<p>Area of Circle given center and a point on circle</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Area of circle with center $(7,-6)$ and passing through $(1.0, -6.0)$ is</td>\n  <td>$113.1$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_coordinate</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.area_of_triangle": {"fullname": "mathgenerator.geometry.area_of_triangle", "modulename": "mathgenerator.geometry", "qualname": "area_of_triangle", "kind": "function", "doc": "<p>Area of Triangle</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Area of triangle with side lengths: $8, 1, 8 = $</td>\n  <td>$3.99$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_a</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_b</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.basic_trigonometry": {"fullname": "mathgenerator.geometry.basic_trigonometry", "modulename": "mathgenerator.geometry", "qualname": "basic_trigonometry", "kind": "function", "doc": "<p>Trigonometric Values</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$\\sin(30) = $</td>\n  <td>$\\frac{1}{2}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">angles</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">30</span><span class=\"p\">,</span> <span class=\"mi\">45</span><span class=\"p\">,</span> <span class=\"mi\">60</span><span class=\"p\">,</span> <span class=\"mi\">90</span><span class=\"p\">]</span>, </span><span class=\"param\"><span class=\"n\">functions</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"s1\">&#39;sin&#39;</span><span class=\"p\">,</span> <span class=\"s1\">&#39;cos&#39;</span><span class=\"p\">,</span> <span class=\"s1\">&#39;tan&#39;</span><span class=\"p\">]</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.circumference": {"fullname": "mathgenerator.geometry.circumference", "modulename": "mathgenerator.geometry", "qualname": "circumference", "kind": "function", "doc": "<p>Circumference of Circle</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Circumference of circle with radius $56 = $</td>\n  <td>$351.86$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.complementary_and_supplementary_angle": {"fullname": "mathgenerator.geometry.complementary_and_supplementary_angle", "modulename": "mathgenerator.geometry", "qualname": "complementary_and_supplementary_angle", "kind": "function", "doc": "<p>Complementary and Supplementary Angle</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>The complementary angle of $15 =$</td>\n  <td>$75$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_supp</span><span class=\"o\">=</span><span class=\"mi\">180</span>, </span><span class=\"param\"><span class=\"n\">max_comp</span><span class=\"o\">=</span><span class=\"mi\">90</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.curved_surface_area_cylinder": {"fullname": "mathgenerator.geometry.curved_surface_area_cylinder", "modulename": "mathgenerator.geometry", "qualname": "curved_surface_area_cylinder", "kind": "function", "doc": "<p>Curved surface area of a cylinder</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>What is the curved surface area of a cylinder of radius, $44$ and height, $92$?</td>\n  <td>$25434.33$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">49</span>, </span><span class=\"param\"><span class=\"n\">max_height</span><span class=\"o\">=</span><span class=\"mi\">99</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.degree_to_rad": {"fullname": "mathgenerator.geometry.degree_to_rad", "modulename": "mathgenerator.geometry", "qualname": "degree_to_rad", "kind": "function", "doc": "<p>Degrees to Radians</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Angle $113$ degrees in radians is:</td>\n  <td>$1.97$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_deg</span><span class=\"o\">=</span><span class=\"mi\">360</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.equation_of_line_from_two_points": {"fullname": "mathgenerator.geometry.equation_of_line_from_two_points", "modulename": "mathgenerator.geometry", "qualname": "equation_of_line_from_two_points", "kind": "function", "doc": "<p>Equation of line from two points</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>What is the equation of the line between points $(13,9)$ and $(6,-19)$ in slope-intercept form?</td>\n  <td>$y = 4x -43$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_coordinate</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">min_coordinate</span><span class=\"o\">=-</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.fourth_angle_of_quadrilateral": {"fullname": "mathgenerator.geometry.fourth_angle_of_quadrilateral", "modulename": "mathgenerator.geometry", "qualname": "fourth_angle_of_quadrilateral", "kind": "function", "doc": "<p>Fourth Angle of Quadrilateral</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Fourth angle of quadrilateral with angles $162 , 43, 78 =$</td>\n  <td>$77$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_angle</span><span class=\"o\">=</span><span class=\"mi\">180</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.perimeter_of_polygons": {"fullname": "mathgenerator.geometry.perimeter_of_polygons", "modulename": "mathgenerator.geometry", "qualname": "perimeter_of_polygons", "kind": "function", "doc": "<p>Perimeter of Polygons</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>The perimeter of a $4$ sided polygon with lengths of $30, 105, 78, 106$cm is:</td>\n  <td>$319$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_sides</span><span class=\"o\">=</span><span class=\"mi\">12</span>, </span><span class=\"param\"><span class=\"n\">max_length</span><span class=\"o\">=</span><span class=\"mi\">120</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.pythagorean_theorem": {"fullname": "mathgenerator.geometry.pythagorean_theorem", "modulename": "mathgenerator.geometry", "qualname": "pythagorean_theorem", "kind": "function", "doc": "<p>Pythagorean Theorem</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>What is the hypotenuse of a right triangle given the other two sides have lengths $9$ and $10$?</td>\n  <td>$13.45$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_length</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.radian_to_deg": {"fullname": "mathgenerator.geometry.radian_to_deg", "modulename": "mathgenerator.geometry", "qualname": "radian_to_deg", "kind": "function", "doc": "<p>Radians to Degrees</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_rad</span><span class=\"o\">=</span><span class=\"mf\">6.28</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.sector_area": {"fullname": "mathgenerator.geometry.sector_area", "modulename": "mathgenerator.geometry", "qualname": "sector_area", "kind": "function", "doc": "<p>Area of a Sector</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>What is the area of a sector with radius $42$ and angle $83$ degrees?</td>\n  <td>$1277.69$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">49</span>, </span><span class=\"param\"><span class=\"n\">max_angle</span><span class=\"o\">=</span><span class=\"mi\">359</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.sum_of_polygon_angles": {"fullname": "mathgenerator.geometry.sum_of_polygon_angles", "modulename": "mathgenerator.geometry", "qualname": "sum_of_polygon_angles", "kind": "function", "doc": "<p>Sum of Angles of Polygon</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>What is the sum of interior angles of a polygon with $8$ sides?</td>\n  <td>$1080$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_sides</span><span class=\"o\">=</span><span class=\"mi\">12</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.surface_area_cone": {"fullname": "mathgenerator.geometry.surface_area_cone", "modulename": "mathgenerator.geometry", "qualname": "surface_area_cone", "kind": "function", "doc": "<p>Surface area of a cone</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Surface area of cone with height $= 26m$ and radius $= 6m$ is</td>\n  <td>$616 m^2$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_height</span><span class=\"o\">=</span><span class=\"mi\">50</span>, </span><span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.surface_area_cube": {"fullname": "mathgenerator.geometry.surface_area_cube", "modulename": "mathgenerator.geometry", "qualname": "surface_area_cube", "kind": "function", "doc": "<p>Surface area of a cube</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Surface area of cube with side $= 6m$ is</td>\n  <td>$216 m^2$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_side</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.surface_area_cuboid": {"fullname": "mathgenerator.geometry.surface_area_cuboid", "modulename": "mathgenerator.geometry", "qualname": "surface_area_cuboid", "kind": "function", "doc": "<p>Surface area of a cuboid</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Surface area of cuboid with sides of lengths: $11m, 20m, 8m$ is</td>\n  <td>$936 m^2$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_side</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.surface_area_cylinder": {"fullname": "mathgenerator.geometry.surface_area_cylinder", "modulename": "mathgenerator.geometry", "qualname": "surface_area_cylinder", "kind": "function", "doc": "<p>Surface area of a cylinder</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Surface area of cylinder with height $= 26m$ and radius $= 15m$ is</td>\n  <td>$3864 m^2$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_height</span><span class=\"o\">=</span><span class=\"mi\">50</span>, </span><span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.surface_area_pyramid": {"fullname": "mathgenerator.geometry.surface_area_pyramid", "modulename": "mathgenerator.geometry", "qualname": "surface_area_pyramid", "kind": "function", "doc": "<p>Surface area of a pyramid</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Surface area of pyramid with base length $= 30m$, base width $= 40m$, and height $= 25m$ is</td>\n  <td>$2400 m^2$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.surface_area_sphere": {"fullname": "mathgenerator.geometry.surface_area_sphere", "modulename": "mathgenerator.geometry", "qualname": "surface_area_sphere", "kind": "function", "doc": "<p>Surface area of a sphere</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Surface area of a sphere with radius $= 8m$ is</td>\n  <td>$804.25 m^2$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_side</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.third_angle_of_triangle": {"fullname": "mathgenerator.geometry.third_angle_of_triangle", "modulename": "mathgenerator.geometry", "qualname": "third_angle_of_triangle", "kind": "function", "doc": "<p>Third Angle of Triangle</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Third angle of triangle with angles $10$ and $22 =$</td>\n  <td>$148$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_angle</span><span class=\"o\">=</span><span class=\"mi\">89</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.valid_triangle": {"fullname": "mathgenerator.geometry.valid_triangle", "modulename": "mathgenerator.geometry", "qualname": "valid_triangle", "kind": "function", "doc": "<p>Valid Triangle</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Does triangel with sides $10, 31$ and $14$ exist?</td>\n  <td>No</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_side_length</span><span class=\"o\">=</span><span class=\"mi\">50</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.volume_cone": {"fullname": "mathgenerator.geometry.volume_cone", "modulename": "mathgenerator.geometry", "qualname": "volume_cone", "kind": "function", "doc": "<p>Volume of a cone</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Volume of cone with height $= 44m$ and radius $= 11m$ is</td>\n  <td>$5575 m^3$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_height</span><span class=\"o\">=</span><span class=\"mi\">50</span>, </span><span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.volume_cube": {"fullname": "mathgenerator.geometry.volume_cube", "modulename": "mathgenerator.geometry", "qualname": "volume_cube", "kind": "function", "doc": "<p>Volume of a cube\n| Ex. Problem | Ex. Solution |\n| --- | --- |\n| Volume of a cube with a side length of $19m$ is | $6859 m^3$ |</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_side</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.volume_cuboid": {"fullname": "mathgenerator.geometry.volume_cuboid", "modulename": "mathgenerator.geometry", "qualname": "volume_cuboid", "kind": "function", "doc": "<p>Volume of a cuboid</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Volume of cuboid with sides = $17m, 11m, 13m$ is</td>\n  <td>$2431 m^3$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_side</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.volume_cylinder": {"fullname": "mathgenerator.geometry.volume_cylinder", "modulename": "mathgenerator.geometry", "qualname": "volume_cylinder", "kind": "function", "doc": "<p>Volume of a cylinder</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Volume of cylinder with height $= 3m$ and radius $= 10m$ is</td>\n  <td>$942 m^3$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_height</span><span class=\"o\">=</span><span class=\"mi\">50</span>, </span><span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.volume_cone_frustum": {"fullname": "mathgenerator.geometry.volume_cone_frustum", "modulename": "mathgenerator.geometry", "qualname": "volume_cone_frustum", "kind": "function", "doc": "<p>Volume of the frustum of a cone</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Volume of frustum with height $= 30m$ and $r1 = 20m$ is and $r2 = 8m$ is</td>\n  <td>$19603.54 m^3$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_r1</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_r2</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_height</span><span class=\"o\">=</span><span class=\"mi\">50</span>, </span><span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.volume_hemisphere": {"fullname": "mathgenerator.geometry.volume_hemisphere", "modulename": "mathgenerator.geometry", "qualname": "volume_hemisphere", "kind": "function", "doc": "<p>Volume of a hemisphere</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Volume of hemisphere with radius $32m =$</td>\n  <td>$68629.14 m^3$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.volume_pyramid": {"fullname": "mathgenerator.geometry.volume_pyramid", "modulename": "mathgenerator.geometry", "qualname": "volume_pyramid", "kind": "function", "doc": "<p>Volume of a pyramid</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Volume of pyramid with base length $= 7 m$, base width $= 18 m$ and height $= 42 m$ is</td>\n  <td>$1764.0 m^3$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_length</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_width</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_height</span><span class=\"o\">=</span><span class=\"mi\">50</span>, </span><span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.geometry.volume_sphere": {"fullname": "mathgenerator.geometry.volume_sphere", "modulename": "mathgenerator.geometry", "qualname": "volume_sphere", "kind": "function", "doc": "<p>Volume of a sphere</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Volume of sphere with radius $30 m = $</td>\n  <td>$113097.36 m^3$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc": {"fullname": "mathgenerator.misc", "modulename": "mathgenerator.misc", "kind": "module", "doc": "<p></p>\n"}, "mathgenerator.misc.arithmetic_progression_sum": {"fullname": "mathgenerator.misc.arithmetic_progression_sum", "modulename": "mathgenerator.misc", "qualname": "arithmetic_progression_sum", "kind": "function", "doc": "<p>Arithmetic Progression Sum</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Find the sum of first $44$ terms of the AP series: $49, 145, 241 ... $</td>\n  <td>$92972.0$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_d</span><span class=\"o\">=</span><span class=\"mi\">100</span>, </span><span class=\"param\"><span class=\"n\">max_a</span><span class=\"o\">=</span><span class=\"mi\">100</span>, </span><span class=\"param\"><span class=\"n\">max_n</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc.arithmetic_progression_term": {"fullname": "mathgenerator.misc.arithmetic_progression_term", "modulename": "mathgenerator.misc", "qualname": "arithmetic_progression_term", "kind": "function", "doc": "<p>Arithmetic Progression Term</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Find term number $12$ of the AP series: $-54, 24, 102 ... $</td>\n  <td>$804$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_d</span><span class=\"o\">=</span><span class=\"mi\">100</span>, </span><span class=\"param\"><span class=\"n\">max_a</span><span class=\"o\">=</span><span class=\"mi\">100</span>, </span><span class=\"param\"><span class=\"n\">max_n</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc.base_conversion": {"fullname": "mathgenerator.misc.base_conversion", "modulename": "mathgenerator.misc", "qualname": "base_conversion", "kind": "function", "doc": "<p>Base Conversion</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Convert $45204$ from base $10$ to base $4$</td>\n  <td>$23002110$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_num</span><span class=\"o\">=</span><span class=\"mi\">60000</span>, </span><span class=\"param\"><span class=\"n\">max_base</span><span class=\"o\">=</span><span class=\"mi\">16</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc.binomial_distribution": {"fullname": "mathgenerator.misc.binomial_distribution", "modulename": "mathgenerator.misc", "qualname": "binomial_distribution", "kind": "function", "doc": "<p>Binomial distribution</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>A manufacturer of metal pistons finds that, on average, $30.56$% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of $20$ pistons will contain no more than $2$ rejected pistons?</td>\n  <td>$3.17$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc.celsius_to_fahrenheit": {"fullname": "mathgenerator.misc.celsius_to_fahrenheit", "modulename": "mathgenerator.misc", "qualname": "celsius_to_fahrenheit", "kind": "function", "doc": "<p>Celsius to Fahrenheit</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Convert $-46$ degrees Celsius to degrees Fahrenheit</td>\n  <td>$-50.8$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_temp</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc.common_factors": {"fullname": "mathgenerator.misc.common_factors", "modulename": "mathgenerator.misc", "qualname": "common_factors", "kind": "function", "doc": "<p>Common Factors</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Common Factors of $100$ and $44 = $</td>\n  <td>$[1, 2, 4]$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc.complex_to_polar": {"fullname": "mathgenerator.misc.complex_to_polar", "modulename": "mathgenerator.misc", "qualname": "complex_to_polar", "kind": "function", "doc": "<p>Complex to polar form</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$19.42(-19.0\\theta + i-4.0\\theta)$</td>\n  <td>$-2.93$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">min_real_imaginary_num</span><span class=\"o\">=-</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_real_imaginary_num</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc.decimal_to_roman_numerals": {"fullname": "mathgenerator.misc.decimal_to_roman_numerals", "modulename": "mathgenerator.misc", "qualname": "decimal_to_roman_numerals", "kind": "function", "doc": "<p>Decimal to Roman Numerals</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>The number $92$ in roman numerals is:</td>\n  <td>$XCII$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_decimal</span><span class=\"o\">=</span><span class=\"mi\">4000</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc.euclidian_norm": {"fullname": "mathgenerator.misc.euclidian_norm", "modulename": "mathgenerator.misc", "qualname": "euclidian_norm", "kind": "function", "doc": "<p>Euclidian norm or L2 norm of a vector</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Euclidian norm or L2 norm of the vector $[659.9225071540442, 243.40887829281564, 128.79950053874424, 263.19226900031344]$ is:</td>\n  <td>$761.97$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">maxEltAmt</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc.factors": {"fullname": "mathgenerator.misc.factors", "modulename": "mathgenerator.misc", "qualname": "factors", "kind": "function", "doc": "<p>Factors of a number</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Factors of $176 = $</td>\n  <td>$[1, 2, 4, 8, 11, 16, 22, 44, 88, 176]$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">1000</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc.geometric_mean": {"fullname": "mathgenerator.misc.geometric_mean", "modulename": "mathgenerator.misc", "qualname": "geometric_mean", "kind": "function", "doc": "<p>Geometric Mean of N Numbers</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Geometric mean of $3$ numbers $[72, 21, 87] = $</td>\n  <td>$50.86$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_value</span><span class=\"o\">=</span><span class=\"mi\">100</span>, </span><span class=\"param\"><span class=\"n\">max_count</span><span class=\"o\">=</span><span class=\"mi\">4</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc.geometric_progression": {"fullname": "mathgenerator.misc.geometric_progression", "modulename": "mathgenerator.misc", "qualname": "geometric_progression", "kind": "function", "doc": "<p>Geometric Progression</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>For the given GP $[11, 44, 176, 704, 2816, 11264]$. Find the value of a common ratio, 7th term value, sum upto 10th term</td>\n  <td>The value of a is $11$, common ratio is $4$ , 7th term is $45056$, sum upto 10th term is $3844775.0$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">number_values</span><span class=\"o\">=</span><span class=\"mi\">6</span>, </span><span class=\"param\"><span class=\"n\">min_value</span><span class=\"o\">=</span><span class=\"mi\">2</span>, </span><span class=\"param\"><span class=\"n\">max_value</span><span class=\"o\">=</span><span class=\"mi\">12</span>, </span><span class=\"param\"><span class=\"n\">n_term</span><span class=\"o\">=</span><span class=\"mi\">7</span>, </span><span class=\"param\"><span class=\"n\">sum_term</span><span class=\"o\">=</span><span class=\"mi\">5</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc.harmonic_mean": {"fullname": "mathgenerator.misc.harmonic_mean", "modulename": "mathgenerator.misc", "qualname": "harmonic_mean", "kind": "function", "doc": "<p>Harmonic Mean of N Numbers</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Harmonic mean of $4$ numbers $52, 56, 25, 57 = $</td>\n  <td>$602.33$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_value</span><span class=\"o\">=</span><span class=\"mi\">100</span>, </span><span class=\"param\"><span class=\"n\">max_count</span><span class=\"o\">=</span><span class=\"mi\">4</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc.is_leap_year": {"fullname": "mathgenerator.misc.is_leap_year", "modulename": "mathgenerator.misc", "qualname": "is_leap_year", "kind": "function", "doc": "<p>Is Leap Year or Not</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Is $2000$ a leap year?</td>\n  <td>$2000$ is a leap year</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">minNumber</span><span class=\"o\">=</span><span class=\"mi\">1900</span>, </span><span class=\"param\"><span class=\"n\">max_number</span><span class=\"o\">=</span><span class=\"mi\">2099</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc.lcm": {"fullname": "mathgenerator.misc.lcm", "modulename": "mathgenerator.misc", "qualname": "lcm", "kind": "function", "doc": "<p>LCM (Least Common Multiple)</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>LCM of $3$ and $18 = $</td>\n  <td>$18$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc.minutes_to_hours": {"fullname": "mathgenerator.misc.minutes_to_hours", "modulename": "mathgenerator.misc", "qualname": "minutes_to_hours", "kind": "function", "doc": "<p>Convert minutes to hours and minutes</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Convert $836$ minutes to hours &amp; minutes</td>\n  <td>$13$ hours and $56$ minutes</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_minutes</span><span class=\"o\">=</span><span class=\"mi\">999</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc.prime_factors": {"fullname": "mathgenerator.misc.prime_factors", "modulename": "mathgenerator.misc", "qualname": "prime_factors", "kind": "function", "doc": "<p>Prime Factors</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Find prime factors of $30$</td>\n  <td>$2, 3, 5$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">min_val</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">200</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc.product_of_scientific_notations": {"fullname": "mathgenerator.misc.product_of_scientific_notations", "modulename": "mathgenerator.misc", "qualname": "product_of_scientific_notations", "kind": "function", "doc": "<p>Product of scientific notations</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Product of scientific notations $5.11 \\times 10^{67}$ and $3.64 \\times 10^{-59} = $</td>\n  <td>$1.86 \\times 10^{9}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">min_exp_val</span><span class=\"o\">=-</span><span class=\"mi\">100</span>, </span><span class=\"param\"><span class=\"n\">max_exp_val</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc.profit_loss_percent": {"fullname": "mathgenerator.misc.profit_loss_percent", "modulename": "mathgenerator.misc", "qualname": "profit_loss_percent", "kind": "function", "doc": "<p>Profit or Loss Percent</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Loss percent when $CP = 751$ and $SP = 290$ is:</td>\n  <td>$61.38$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_cp</span><span class=\"o\">=</span><span class=\"mi\">1000</span>, </span><span class=\"param\"><span class=\"n\">max_sp</span><span class=\"o\">=</span><span class=\"mi\">1000</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc.quotient_of_power_same_base": {"fullname": "mathgenerator.misc.quotient_of_power_same_base", "modulename": "mathgenerator.misc", "qualname": "quotient_of_power_same_base", "kind": "function", "doc": "<p>Quotient of Powers with Same Base</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>The Quotient of $5^{6}$ and $5^{8} = $5^{6-8} = 5^{-2}$</td>\n  <td>$0.04$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_base</span><span class=\"o\">=</span><span class=\"mi\">50</span>, </span><span class=\"param\"><span class=\"n\">max_power</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc.quotient_of_power_same_power": {"fullname": "mathgenerator.misc.quotient_of_power_same_power", "modulename": "mathgenerator.misc", "qualname": "quotient_of_power_same_power", "kind": "function", "doc": "<p>Quotient of Powers with Same Power</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>The quotient of $19^{8}$ and $10^{8} = (19/10)^8 = 1.9^{8}$</td>\n  <td>$169.84$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_base</span><span class=\"o\">=</span><span class=\"mi\">50</span>, </span><span class=\"param\"><span class=\"n\">max_power</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc.set_operation": {"fullname": "mathgenerator.misc.set_operation", "modulename": "mathgenerator.misc", "qualname": "set_operation", "kind": "function", "doc": "<p>Union, Intersection, Difference of Two Sets</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Given the two sets $a={1, 2, 4, 5}$, $b={8, 1, 2}. Find the Union, intersection, a-b, b-a, and symmetric difference</td>\n  <td>Union is ${1, 2, 4, 5, 8}$. Intersection is ${1, 2}$, a-b is ${4, 5}$, b-a is ${8}$. Symmetric difference is ${4, 5, 8}$.</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">min_size</span><span class=\"o\">=</span><span class=\"mi\">3</span>, </span><span class=\"param\"><span class=\"n\">max_size</span><span class=\"o\">=</span><span class=\"mi\">7</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc.signum_function": {"fullname": "mathgenerator.misc.signum_function", "modulename": "mathgenerator.misc", "qualname": "signum_function", "kind": "function", "doc": "<p>Signum Function</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Signum of $-229$ is =</td>\n  <td>$-1$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"nb\">min</span><span class=\"o\">=-</span><span class=\"mi\">999</span>, </span><span class=\"param\"><span class=\"nb\">max</span><span class=\"o\">=</span><span class=\"mi\">999</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.misc.surds_comparison": {"fullname": "mathgenerator.misc.surds_comparison", "modulename": "mathgenerator.misc", "qualname": "surds_comparison", "kind": "function", "doc": "<p>Comparing Surds</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Fill in the blanks $42^{\\frac{1}{2}}$ _ $45^{\\frac{1}{5}}$</td>\n  <td>$&gt;$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_value</span><span class=\"o\">=</span><span class=\"mi\">100</span>, </span><span class=\"param\"><span class=\"n\">max_root</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.statistics": {"fullname": "mathgenerator.statistics", "modulename": "mathgenerator.statistics", "kind": "module", "doc": "<p></p>\n"}, "mathgenerator.statistics.combinations": {"fullname": "mathgenerator.statistics.combinations", "modulename": "mathgenerator.statistics", "qualname": "combinations", "kind": "function", "doc": "<p>Combinations of Objects</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Find the number of combinations from $19$ objects picked $6$ at a time.</td>\n  <td>$27132$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_lengthgth</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.statistics.conditional_probability": {"fullname": "mathgenerator.statistics.conditional_probability", "modulename": "mathgenerator.statistics", "qualname": "conditional_probability", "kind": "function", "doc": "<p>Conditional Probability</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Someone tested positive for a nasty disease which only $1.18$% of the population have. Test sensitivity (true positive) is equal to $SN=98.73$% whereas test specificity (true negative) $SP=99.99$%. What is the probability that this guy really has that disease?</td>\n  <td>$99.16$%</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.statistics.confidence_interval": {"fullname": "mathgenerator.statistics.confidence_interval", "modulename": "mathgenerator.statistics", "qualname": "confidence_interval", "kind": "function", "doc": "<p>Confidence interval For sample S</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>The confidence interval for sample $[234, 223, 210, 203, 258, 299, 281, 208, 278, 252, 295, 245, 280, 235, 219, 297, 214, 267, 212, 256, 232, 221]$ with $99$% confidence is</td>\n  <td>$(263.31, 229.33)$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.statistics.data_summary": {"fullname": "mathgenerator.statistics.data_summary", "modulename": "mathgenerator.statistics", "qualname": "data_summary", "kind": "function", "doc": "<p>Mean, Standard Deviation and Variance</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Find the mean,standard deviation and variance for the data $9, 29, 46, 27, 46, 15, 10, 44, 19, 33, 38, 7, 34, 28, 8$</td>\n  <td>The Mean is $26.2$, Standard Deviation is $186.29$, Variance is $13.65$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">number_values</span><span class=\"o\">=</span><span class=\"mi\">15</span>, </span><span class=\"param\"><span class=\"n\">min_val</span><span class=\"o\">=</span><span class=\"mi\">5</span>, </span><span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">50</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.statistics.dice_sum_probability": {"fullname": "mathgenerator.statistics.dice_sum_probability", "modulename": "mathgenerator.statistics", "qualname": "dice_sum_probability", "kind": "function", "doc": "<p>Probability of a certain sum appearing on faces of dice</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>If $2$ dice are rolled at the same time, the probability of getting a sum of $5 =$</td>\n  <td>$\frac{4}{36}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_dice</span><span class=\"o\">=</span><span class=\"mi\">3</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.statistics.mean_median": {"fullname": "mathgenerator.statistics.mean_median", "modulename": "mathgenerator.statistics", "qualname": "mean_median", "kind": "function", "doc": "<p>Mean and Median</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Given the series of numbers $[4, 19, 21, 22, 43, 44, 60, 81, 87, 92]$. Find the arithmatic mean and median of the series</td>\n  <td>Arithmetic mean of the series is $47.3$ and arithmetic median of this series is $43.5$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_length</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "mathgenerator.statistics.permutation": {"fullname": "mathgenerator.statistics.permutation", "modulename": "mathgenerator.statistics", "qualname": "permutation", "kind": "function", "doc": "<p>Permutations</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Number of Permutations from $18$ objects picked $5$ at a time is:</td>\n  <td>$1028160$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_lengthgth</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}}, "docInfo": {"mathgenerator": {"qualname": 0, "fullname": 1, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 563}, "mathgenerator.get_gen_list": {"qualname": 3, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 7, "bases": 0, "doc": 3}, "mathgenerator.gen_by_id": {"qualname": 3, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 25, "bases": 0, "doc": 3}, "mathgenerator.getGenList": {"qualname": 1, "fullname": 2, "annotation": 0, "default_value": 0, "signature": 7, "bases": 0, "doc": 3}, 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+    /** pdoc search index */const docs = [{"fullname": "mathgenerator", "modulename": "mathgenerator", "kind": "module", "doc": "<h1 id=\"mathgenerator\">mathgenerator</h1>\n\n<p>A math problem generator, created for the purpose of giving teachers and students the means to easily get access to random math exercises to suit their needs.</p>\n\n<p>To try out generators, go to <a href=\"https://mathgenerator-demo.netlify.app\">https://mathgenerator-demo.netlify.app</a></p>\n\n<p>See <a href=\"https://github.com/lukew3/mathgenerator/blob/main/CONTRIBUTING.md\">CONTRIBUTING.md</a> for information about how to contribute.</p>\n\n<h2 id=\"table-of-contents\">Table of Contents</h2>\n\n<ul>\n<li><a href=\"#installation\">Installation</a></li>\n<li><a href=\"#usage\">Usage</a></li>\n<li><a href=\"#documentation\">Documentation</a></li>\n</ul>\n\n<h2 id=\"installation\">Installation</h2>\n\n<p>The project can be install via pip</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code>pip<span class=\"w\"> </span>install<span class=\"w\"> </span>mathgenerator\n</code></pre>\n</div>\n\n<h2 id=\"usage\">Usage</h2>\n\n<p>Here is an example of how you would generate an addition problem:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span> <span class=\"nn\">mathgenerator</span>\n\n<span class=\"c1\">#generate an addition problem</span>\n<span class=\"n\">problem</span><span class=\"p\">,</span> <span class=\"n\">solution</span> <span class=\"o\">=</span> <span class=\"n\">mathgenerator</span><span class=\"o\">.</span><span class=\"n\">addition</span><span class=\"p\">()</span>\n\n<span class=\"c1\">#another way to generate an addition problem using genById()</span>\n<span class=\"n\">problem</span><span class=\"p\">,</span> <span class=\"n\">solution</span> <span class=\"o\">=</span> <span class=\"n\">mathgenerator</span><span class=\"o\">.</span><span class=\"n\">genById</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>You may prefer to use <code>import mathgenerator as mg</code> and run functions like <code>mg.addition()</code> so that you don't have to type as much.\n<!--</p>\n\n<h3 id=\"creating-a-worksheet\">Creating a worksheet</h3>\n\n<p>If you wish to create a worksheet, you can use the <a href=\"https://github.com/lukew3/worksheetgen\">worksheetgen</a> package. Install this with <code>pip install worksheetgen</code>. Here is an example of how a worksheet would be generated.</p>\n\n<pre><code>from mathgenerator import mathgen\nfrom worksheetgen.wg import Worksheet\n\nws = Worksheet(\"Worksheet title\")\nwith ws.section('Section 1', description='These are instructions')\n    # Writes 10 problems generated with id 1, [0] at the end specifies to take problem, and not solution.\n    for _ in range(10):\n        ws.add_problem(mathgen.genById(1)[0])\nws.write_pdf()\n</code></pre>\n\n<p>This creates the pdf <code>ws.pdf</code> in your current directory\n-->\nProblem/solution pairs are generated with either:</p>\n\n<ul>\n<li><code>mathgenerator.&lt;generator_name&gt;()</code> - generates a problem, solution set from the given generator name.</li>\n<li><code>mathgenerator.genById(id)</code> - generates a problem, solution set with generator id provided by the <code>id</code> parameter</li>\n</ul>\n\n<p><!--</p>\n\n<h4 id=\"format-kwarg\"><code>format</code> kwarg</h4>\n\n<ul>\n<li>Pass <code>format=latex</code> to return problem and solution set as latex. If latex is not available for that generator, the problem will return the string \"Latex unavailable\"</li>\n<li>Pass <code>format=raw</code> to return just the raw data for each generator. An array of each variable necessary to the generator is returned.</li>\n<li>If you don't pass a value to the format kwarg, the generator will return a problem and answer in asciimath format.\n-->\nYou can also use <code>getGenList()</code> to return a list of all generators included in the library in the format:</li>\n</ul>\n\n<pre><code>[funcname, subjectname]\n</code></pre>\n\n<h2 id=\"documentation\">Documentation</h2>\n\n<p>Documentation can be found at <a href=\"https://lukew3.github.io/mathgenerator\">https://lukew3.github.io/mathgenerator</a></p>\n"}, {"fullname": "mathgenerator.get_gen_list", "modulename": "mathgenerator", "qualname": "get_gen_list", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.gen_by_id", "modulename": "mathgenerator", "qualname": "gen_by_id", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"nb\">id</span>, </span><span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.getGenList", "modulename": "mathgenerator", "qualname": "getGenList", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.genById", "modulename": "mathgenerator", "qualname": "genById", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"nb\">id</span>, </span><span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.algebra", "modulename": "mathgenerator.algebra", "kind": "module", "doc": "<p></p>\n"}, {"fullname": "mathgenerator.algebra.basic_algebra", "modulename": "mathgenerator.algebra", "qualname": "basic_algebra", "kind": "function", "doc": "<p>Basic Algebra</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$1x + 5 = 5$</td>\n  <td>$0$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_variable</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.algebra.combine_like_terms", "modulename": "mathgenerator.algebra", "qualname": "combine_like_terms", "kind": "function", "doc": "<p>Combine Like Terms</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$6x^{9} + 3x^{2} + 5x^{19} + 3x^{17}$</td>\n  <td>$3x^{2} + 6x^{9} + 3x^{17} + 5x^{19}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_coef</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">max_exp</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_terms</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.algebra.complex_quadratic", "modulename": "mathgenerator.algebra", "qualname": "complex_quadratic", "kind": "function", "doc": "<p>Complex Quadratic Equation</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Find the roots of given Quadratic Equation $x^2 + 8x + 8 = 0$</td>\n  <td>$((-1.172, -6.828)) = (\\frac{-8 + \\sqrt{32}}{2}, (\\frac{-8 - \\sqrt{32}}{2})$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">prob_type</span><span class=\"o\">=</span><span class=\"mi\">0</span>, </span><span class=\"param\"><span class=\"n\">max_range</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.algebra.compound_interest", "modulename": "mathgenerator.algebra", "qualname": "compound_interest", "kind": "function", "doc": "<p>Compound Interest</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Compound interest for a principle amount of $2679$ dollars, $9$% rate of interest and for a time period of $3$ years is $=$</td>\n  <td>$3469.38$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_principle</span><span class=\"o\">=</span><span class=\"mi\">10000</span>, </span><span class=\"param\"><span class=\"n\">max_rate</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">max_time</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.algebra.distance_two_points", "modulename": "mathgenerator.algebra", "qualname": "distance_two_points", "kind": "function", "doc": "<p>Distance between 2 points</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Find the distance between $(-19, -6)$ and $(15, -16)$</td>\n  <td>$\\sqrt{1256}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_val_xy</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">min_val_xy</span><span class=\"o\">=-</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.algebra.expanding", "modulename": "mathgenerator.algebra", "qualname": "expanding", "kind": "function", "doc": "<p>Expanding Factored Binomial</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$(x-6)(-3x-3)$</td>\n  <td>$x^2+18x+18$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">range_x1</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">range_x2</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">range_a</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">range_b</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.algebra.factoring", "modulename": "mathgenerator.algebra", "qualname": "factoring", "kind": "function", "doc": "<p>Factoring Quadratic\nGiven a quadratic equation in the form x^2 + bx + c, factor it into it's roots (x - x1)(x -x2)</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$x^2+2x-24$</td>\n  <td>$(x-4)(x+6)$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">range_x1</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">range_x2</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.algebra.int_matrix_22_determinant", "modulename": "mathgenerator.algebra", "qualname": "int_matrix_22_determinant", "kind": "function", "doc": "<p>Determinant to 2x2 Matrix</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$\\det \\begin{bmatrix} 88 &amp; 40 \\\\ 9 &amp; 91 \\end{bmatrix}= $</td>\n  <td>$7648$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_matrix_val</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.algebra.intersection_of_two_lines", "modulename": "mathgenerator.algebra", "qualname": "intersection_of_two_lines", "kind": "function", "doc": "<p>Intersection of two lines</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Find the point of intersection of the two lines: $y = \\frac{-2}{6}x + 3$ and $y = \\frac{3}{6}x - 8$</td>\n  <td>$(\\frac{66}{5}, \\frac{-7}{5})$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">min_m</span><span class=\"o\">=-</span><span class=\"mi\">10</span>,</span><span class=\"param\">\t<span class=\"n\">max_m</span><span class=\"o\">=</span><span class=\"mi\">10</span>,</span><span class=\"param\">\t<span class=\"n\">min_b</span><span class=\"o\">=-</span><span class=\"mi\">10</span>,</span><span class=\"param\">\t<span class=\"n\">max_b</span><span class=\"o\">=</span><span class=\"mi\">10</span>,</span><span class=\"param\">\t<span class=\"n\">min_denominator</span><span class=\"o\">=</span><span class=\"mi\">1</span>,</span><span class=\"param\">\t<span class=\"n\">max_denominator</span><span class=\"o\">=</span><span class=\"mi\">6</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.algebra.invert_matrix", "modulename": "mathgenerator.algebra", "qualname": "invert_matrix", "kind": "function", "doc": "<p>Invert Matrix</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Inverse of Matrix $\\begin{bmatrix} 4 &amp; 1 &amp; 4 \\\\ 5 &amp; 1 &amp; 5 \\\\ 12 &amp; 3 &amp; 13 \\end{bmatrix}$ is:</td>\n  <td>$\\begin{bmatrix} 2 &amp; 1 &amp; -1 \\\\ 5 &amp; -4 &amp; 0 \\\\ -3 &amp; 0 &amp; 1 \\end{bmatrix}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">square_matrix_dimension</span><span class=\"o\">=</span><span class=\"mi\">3</span>,</span><span class=\"param\">\t<span class=\"n\">max_matrix_element</span><span class=\"o\">=</span><span class=\"mi\">99</span>,</span><span class=\"param\">\t<span class=\"n\">only_integer_elements_in_inverted_matrixe</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.algebra.linear_equations", "modulename": "mathgenerator.algebra", "qualname": "linear_equations", "kind": "function", "doc": "<p>Linear Equations</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Given the equations $10x + -20y = 310$ and $-16x + -17y = 141$, solve for $x$ and $y$</td>\n  <td>$x = 5$, $y = -13$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">n</span><span class=\"o\">=</span><span class=\"mi\">2</span>, </span><span class=\"param\"><span class=\"n\">var_range</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">coeff_range</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.algebra.line_equation_from_2_points", "modulename": "mathgenerator.algebra", "qualname": "line_equation_from_2_points", "kind": "function", "doc": "<p>Equation of Line from Two Points</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Find the equation of the line passing through the points $(-19,-8)$ and $(-2,0)$.</td>\n  <td>$y=\\frac{8}{17}x+\\frac{16}{17}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.algebra.log", "modulename": "mathgenerator.algebra", "qualname": "log", "kind": "function", "doc": "<p>Logarithm</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$log_{3}(243)=$</td>\n  <td>$5$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_base</span><span class=\"o\">=</span><span class=\"mi\">3</span>, </span><span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">8</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.algebra.matrix_multiplication", "modulename": "mathgenerator.algebra", "qualname": "matrix_multiplication", "kind": "function", "doc": "<p>Multiply Two Matrices</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Multiply $\\begin{bmatrix} 15 &amp; 72 \\\\ 64 &amp; -20 \\\\ 18 &amp; 59 \\\\ -21 &amp; -55 \\\\ 20 &amp; -12 \\\\ -75 &amp; -42 \\\\ 47 &amp; 89 \\\\ -53 &amp; 27 \\\\ -56 &amp; 44 \\end{bmatrix}$ and $\\begin{bmatrix} 49 &amp; -2 &amp; 68 &amp; -28 \\\\ 49 &amp; 6 &amp; 83 &amp; 42 \\end{bmatrix}$</td>\n  <td>$\\begin{bmatrix} 4263 &amp; 402 &amp; 6996 &amp; 2604 \\\\ 2156 &amp; -248 &amp; 2692 &amp; -2632 \\\\ 3773 &amp; 318 &amp; 6121 &amp; 1974 \\\\ -3724 &amp; -288 &amp; -5993 &amp; -1722 \\\\ 392 &amp; -112 &amp; 364 &amp; -1064 \\\\ -5733 &amp; -102 &amp; -8586 &amp; 336 \\\\ 6664 &amp; 440 &amp; 10583 &amp; 2422 \\\\ -1274 &amp; 268 &amp; -1363 &amp; 2618 \\\\ -588 &amp; 376 &amp; -156 &amp; 3416 \\end{bmatrix}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">100</span>, </span><span class=\"param\"><span class=\"n\">max_dim</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.algebra.midpoint_of_two_points", "modulename": "mathgenerator.algebra", "qualname": "midpoint_of_two_points", "kind": "function", "doc": "<p>Midpoint of two points</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>The midpoint of $(-8,10)$ and $(18,0) = $</td>\n  <td>$(5.0,5.0)$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_value</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.algebra.multiply_complex_numbers", "modulename": "mathgenerator.algebra", "qualname": "multiply_complex_numbers", "kind": "function", "doc": "<p>Multiplication of 2 complex numbers</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$(14+18j) * (14+15j) = $</td>\n  <td>$(-74+462j)$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">min_real_imaginary_num</span><span class=\"o\">=-</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_real_imaginary_num</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.algebra.multiply_int_to_22_matrix", "modulename": "mathgenerator.algebra", "qualname": "multiply_int_to_22_matrix", "kind": "function", "doc": "<p>Multiply Integer to 2x2 Matrix</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$5 * \\begin{bmatrix} 1 &amp; 0 \\\\ 2 &amp; 9 \\end{bmatrix} =$</td>\n  <td>$\\begin{bmatrix} 5 &amp; 0 \\\\ 10 &amp; 45 \\end{bmatrix}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_matrix_val</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">max_res</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.algebra.quadratic_equation", "modulename": "mathgenerator.algebra", "qualname": "quadratic_equation", "kind": "function", "doc": "<p>Quadratic Equation</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>What are the zeros of the quadratic equation $22x^2+137x+25=0$</td>\n  <td>${-0.19, -6.04}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.algebra.simple_interest", "modulename": "mathgenerator.algebra", "qualname": "simple_interest", "kind": "function", "doc": "<p>Simple Interest</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Simple interest for a principle amount of $7217$ dollars, $3$% rate of interest and for a time period of $10$ years is $=$</td>\n  <td>$2165.1$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_principle</span><span class=\"o\">=</span><span class=\"mi\">10000</span>, </span><span class=\"param\"><span class=\"n\">max_rate</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">max_time</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.algebra.system_of_equations", "modulename": "mathgenerator.algebra", "qualname": "system_of_equations", "kind": "function", "doc": "<p>Solve a System of Equations in R^2</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Given $-x + 5y = -28$ and $9x + 2y = 64$, solve for $x$ and $y$.</td>\n  <td>$x = 8$, $y = -4$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">range_x</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">range_y</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">coeff_mult_range</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.algebra.vector_cross", "modulename": "mathgenerator.algebra", "qualname": "vector_cross", "kind": "function", "doc": "<p>Cross product of 2 vectors</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$[-1, -4, 10] \\times [-11, 1, -16] = $</td>\n  <td>$[54, -126, -45]$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">min_val</span><span class=\"o\">=-</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.algebra.vector_dot", "modulename": "mathgenerator.algebra", "qualname": "vector_dot", "kind": "function", "doc": "<p>Dot product of 2 vectors</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$[12, -9, -8]\\cdot[-9, 8, 1]=$</td>\n  <td>$-188$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">min_val</span><span class=\"o\">=-</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.algebra.orthogonal_projection", "modulename": "mathgenerator.algebra", "qualname": "orthogonal_projection", "kind": "function", "doc": "<p>Orthogonal Projection</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Find the orthogonal projection of $[2, 3]$ onto $[4, -7]$</td>\n  <td>$[\\frac{-4}{5}, \\frac{7}{5}]$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">min_val</span><span class=\"o\">=-</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.basic_math", "modulename": "mathgenerator.basic_math", "kind": "module", "doc": "<p></p>\n"}, {"fullname": "mathgenerator.basic_math.absolute_difference", "modulename": "mathgenerator.basic_math", "qualname": "absolute_difference", "kind": "function", "doc": "<p>Absolute difference between two numbers</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$|22-34|=$</td>\n  <td>$12$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_a</span><span class=\"o\">=</span><span class=\"mi\">100</span>, </span><span class=\"param\"><span class=\"n\">max_b</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.basic_math.addition", "modulename": "mathgenerator.basic_math", "qualname": "addition", "kind": "function", "doc": "<p>Addition of two numbers</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$22+34=$</td>\n  <td>$56$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_sum</span><span class=\"o\">=</span><span class=\"mi\">99</span>, </span><span class=\"param\"><span class=\"n\">max_addend</span><span class=\"o\">=</span><span class=\"mi\">50</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.basic_math.compare_fractions", "modulename": "mathgenerator.basic_math", "qualname": "compare_fractions", "kind": "function", "doc": "<p>Compare Fractions</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Which symbol represents the comparison between $\\frac{1}{2}$ and $\\frac{3}{4}$?</td>\n  <td>$&gt;$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.basic_math.cube_root", "modulename": "mathgenerator.basic_math", "qualname": "cube_root", "kind": "function", "doc": "<p>Cube Root</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>What is the cube root of: $\\sqrt[3]{125}=$ to 2 decimal places?</td>\n  <td>$5$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">min_no</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">max_no</span><span class=\"o\">=</span><span class=\"mi\">1000</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.basic_math.divide_fractions", "modulename": "mathgenerator.basic_math", "qualname": "divide_fractions", "kind": "function", "doc": "<p>Divide Fractions</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$\\frac{7}{9}\\div\\frac{4}{1}=$</td>\n  <td>$\\frac{7}{36}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.basic_math.division", "modulename": "mathgenerator.basic_math", "qualname": "division", "kind": "function", "doc": "<p>Division</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$216\\div24=$</td>\n  <td>$9$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_a</span><span class=\"o\">=</span><span class=\"mi\">25</span>, </span><span class=\"param\"><span class=\"n\">max_b</span><span class=\"o\">=</span><span class=\"mi\">25</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.basic_math.exponentiation", "modulename": "mathgenerator.basic_math", "qualname": "exponentiation", "kind": "function", "doc": "<p>Exponentiation</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$9^{5}=$</td>\n  <td>$8$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_base</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_expo</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.basic_math.factorial", "modulename": "mathgenerator.basic_math", "qualname": "factorial", "kind": "function", "doc": "<p>Factorial</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$4! =$</td>\n  <td>$24$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_input</span><span class=\"o\">=</span><span class=\"mi\">6</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.basic_math.fraction_multiplication", "modulename": "mathgenerator.basic_math", "qualname": "fraction_multiplication", "kind": "function", "doc": "<p>Fraction Multiplication</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$\\frac{3}{10}\\cdot\\frac{6}{7}=$</td>\n  <td>$\\frac{9}{35}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.basic_math.fraction_to_decimal", "modulename": "mathgenerator.basic_math", "qualname": "fraction_to_decimal", "kind": "function", "doc": "<p>Fraction to Decimal</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$83\\div80=$</td>\n  <td>$1.04$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_res</span><span class=\"o\">=</span><span class=\"mi\">99</span>, </span><span class=\"param\"><span class=\"n\">max_divid</span><span class=\"o\">=</span><span class=\"mi\">99</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.basic_math.greatest_common_divisor", "modulename": "mathgenerator.basic_math", "qualname": "greatest_common_divisor", "kind": "function", "doc": "<p>Greatest Common Divisor of N Numbers ( GCD / HCF )</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$GCD(488075608, 75348096)=$</td>\n  <td>$8$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">numbers_count</span><span class=\"o\">=</span><span class=\"mi\">2</span>, </span><span class=\"param\"><span class=\"n\">max_num</span><span class=\"o\">=</span><span class=\"mi\">1000</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.basic_math.is_composite", "modulename": "mathgenerator.basic_math", "qualname": "is_composite", "kind": "function", "doc": "<p>Is Composite</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Is $171$ composite?</td>\n  <td>Yes</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_num</span><span class=\"o\">=</span><span class=\"mi\">250</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.basic_math.is_prime", "modulename": "mathgenerator.basic_math", "qualname": "is_prime", "kind": "function", "doc": "<p>Is Prime</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Is $37$ prime?</td>\n  <td>Yes</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_num</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.basic_math.multiplication", "modulename": "mathgenerator.basic_math", "qualname": "multiplication", "kind": "function", "doc": "<p>Multiplication</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$10\\cdot9=$</td>\n  <td>$90$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_multi</span><span class=\"o\">=</span><span class=\"mi\">12</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.basic_math.percentage", "modulename": "mathgenerator.basic_math", "qualname": "percentage", "kind": "function", "doc": "<p>Percentage of a number</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>What is $45$% of $39$?</td>\n  <td>$17.55$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_value</span><span class=\"o\">=</span><span class=\"mi\">99</span>, </span><span class=\"param\"><span class=\"n\">max_percentage</span><span class=\"o\">=</span><span class=\"mi\">99</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.basic_math.percentage_difference", "modulename": "mathgenerator.basic_math", "qualname": "percentage_difference", "kind": "function", "doc": "<p>Percentage difference between two numbers</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>What is the percentage difference between $2$ and $10$?</td>\n  <td>$133.33$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_value</span><span class=\"o\">=</span><span class=\"mi\">200</span>, </span><span class=\"param\"><span class=\"n\">min_value</span><span class=\"o\">=</span><span class=\"mi\">0</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.basic_math.percentage_error", "modulename": "mathgenerator.basic_math", "qualname": "percentage_error", "kind": "function", "doc": "<p>Percentage error</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Find the percentage error when observed value equals $32$ and exact value equals $81$.</td>\n  <td>$60.49$%</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_value</span><span class=\"o\">=</span><span class=\"mi\">100</span>, </span><span class=\"param\"><span class=\"n\">min_value</span><span class=\"o\">=-</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.basic_math.power_of_powers", "modulename": "mathgenerator.basic_math", "qualname": "power_of_powers", "kind": "function", "doc": "<p>Power of Powers</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Simplify $18^{10^{8}}$</td>\n  <td>$18^{80}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_base</span><span class=\"o\">=</span><span class=\"mi\">50</span>, </span><span class=\"param\"><span class=\"n\">max_power</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.basic_math.square", "modulename": "mathgenerator.basic_math", "qualname": "square", "kind": "function", "doc": "<p>Square</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$17^2=$</td>\n  <td>$289$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_square_num</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.basic_math.square_root", "modulename": "mathgenerator.basic_math", "qualname": "square_root", "kind": "function", "doc": "<p>Square Root</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$\\sqrt{64}=$</td>\n  <td>$8$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">min_no</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">max_no</span><span class=\"o\">=</span><span class=\"mi\">12</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.basic_math.simplify_square_root", "modulename": "mathgenerator.basic_math", "qualname": "simplify_square_root", "kind": "function", "doc": "<p>Simplify Square Root</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$\\sqrt{63}$</td>\n  <td>$3\\sqrt{7}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_variable</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.basic_math.subtraction", "modulename": "mathgenerator.basic_math", "qualname": "subtraction", "kind": "function", "doc": "<p>Subtraction of two numbers</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$54-22=$</td>\n  <td>$32$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_minuend</span><span class=\"o\">=</span><span class=\"mi\">99</span>, </span><span class=\"param\"><span class=\"n\">max_diff</span><span class=\"o\">=</span><span class=\"mi\">99</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.calculus", "modulename": "mathgenerator.calculus", "kind": "module", "doc": "<p></p>\n"}, {"fullname": "mathgenerator.calculus.definite_integral", "modulename": "mathgenerator.calculus", "qualname": "definite_integral", "kind": "function", "doc": "<p>Definite Integral of Quadratic Equation</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>The definite integral within limits $0$ to $1$ of the equation $28x^2 + 32x + 66 = $</td>\n  <td>$91.33$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_coef</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.calculus.power_rule_differentiation", "modulename": "mathgenerator.calculus", "qualname": "power_rule_differentiation", "kind": "function", "doc": "<p>Power Rule Differentiation</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Differentiate $1x^{5} + 4x^{7} + 4x^{4}$</td>\n  <td>$5x^{4} + 28x^{6} + 16x^{3}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_coef</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">max_exp</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">max_terms</span><span class=\"o\">=</span><span class=\"mi\">5</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.calculus.power_rule_integration", "modulename": "mathgenerator.calculus", "qualname": "power_rule_integration", "kind": "function", "doc": "<p>Power Rule Integration</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Integrate $9x^{6} + 2x^{6} + 4x^{3}$</td>\n  <td>$\\frac{9}{6}x^{7} + \\frac{2}{6}x^{7} + \\frac{4}{3}x^{4} + C$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_coef</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">max_exp</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">max_terms</span><span class=\"o\">=</span><span class=\"mi\">5</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.calculus.stationary_points", "modulename": "mathgenerator.calculus", "qualname": "stationary_points", "kind": "function", "doc": "<p>Stationary Points</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$f(x)=6x^3 + 6x^2 + x + 8$</td>\n  <td>${- \\frac{1}{3} - \\frac{\\sqrt{2}}{6}, - \\frac{1}{3} + \\frac{\\sqrt{2}}{6}}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_exp</span><span class=\"o\">=</span><span class=\"mi\">3</span>, </span><span class=\"param\"><span class=\"n\">max_coef</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.calculus.trig_differentiation", "modulename": "mathgenerator.calculus", "qualname": "trig_differentiation", "kind": "function", "doc": "<p>Trigonometric Differentiation</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$\\frac{d}{dx}(\\csc)=$</td>\n  <td>$-\\csc \\cdot \\cot$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.computer_science", "modulename": "mathgenerator.computer_science", "kind": "module", "doc": "<p></p>\n"}, {"fullname": "mathgenerator.computer_science.bcd_to_decimal", "modulename": "mathgenerator.computer_science", "qualname": "bcd_to_decimal", "kind": "function", "doc": "<p>Binary Coded Decimal to Integer</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Integer of Binary Coded Decimal $4 =$</td>\n  <td>$17801$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_number</span><span class=\"o\">=</span><span class=\"mi\">10000</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.computer_science.binary_2s_complement", "modulename": "mathgenerator.computer_science", "qualname": "binary_2s_complement", "kind": "function", "doc": "<p>Binary 2's Complement</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>2's complement of $1011 = $</td>\n  <td>$101$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">maxDigits</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.computer_science.binary_complement_1s", "modulename": "mathgenerator.computer_science", "qualname": "binary_complement_1s", "kind": "function", "doc": "<p>Binary Complement 1s</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$1111001 = $</td>\n  <td>$0000110$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">maxDigits</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.computer_science.binary_to_decimal", "modulename": "mathgenerator.computer_science", "qualname": "binary_to_decimal", "kind": "function", "doc": "<p>Binary to Decimal</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$000110$</td>\n  <td>$6$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_dig</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.computer_science.binary_to_hex", "modulename": "mathgenerator.computer_science", "qualname": "binary_to_hex", "kind": "function", "doc": "<p>Binary to Hexidecimal</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$010101$</td>\n  <td>$0x15$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_dig</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.computer_science.decimal_to_bcd", "modulename": "mathgenerator.computer_science", "qualname": "decimal_to_bcd", "kind": "function", "doc": "<p>Decimal to Binary Coded Decimal</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>BCD of Decimal Number $6575 = $</td>\n  <td>$191015$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_number</span><span class=\"o\">=</span><span class=\"mi\">10000</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.computer_science.decimal_to_binary", "modulename": "mathgenerator.computer_science", "qualname": "decimal_to_binary", "kind": "function", "doc": "<p>Decimal to Binary</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Binary of $4 = $</td>\n  <td>$100$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_dec</span><span class=\"o\">=</span><span class=\"mi\">99</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.computer_science.decimal_to_hexadeci", "modulename": "mathgenerator.computer_science", "qualname": "decimal_to_hexadeci", "kind": "function", "doc": "<p>Decimal to Hexadecimal</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Hexadecimal of $410 = $</td>\n  <td>$0x19a$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_dec</span><span class=\"o\">=</span><span class=\"mi\">1000</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.computer_science.decimal_to_octal", "modulename": "mathgenerator.computer_science", "qualname": "decimal_to_octal", "kind": "function", "doc": "<p>Decimal to Octal</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>The decimal number $3698$ in octal is:</td>\n  <td>$0o7162$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_decimal</span><span class=\"o\">=</span><span class=\"mi\">4096</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.computer_science.fibonacci_series", "modulename": "mathgenerator.computer_science", "qualname": "fibonacci_series", "kind": "function", "doc": "<p>Fibonacci Series</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>The Fibonacci Series of the first ${n}$ numbers is ?</td>\n  <td>$0, 1, 1, 2, 3, 5, 8, 13, 21$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">min_no</span><span class=\"o\">=</span><span class=\"mi\">1</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.computer_science.modulo_division", "modulename": "mathgenerator.computer_science", "qualname": "modulo_division", "kind": "function", "doc": "<p>Modulo Division</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$43$ % $33 = $</td>\n  <td>$10$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_res</span><span class=\"o\">=</span><span class=\"mi\">99</span>, </span><span class=\"param\"><span class=\"n\">max_modulo</span><span class=\"o\">=</span><span class=\"mi\">99</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.computer_science.nth_fibonacci_number", "modulename": "mathgenerator.computer_science", "qualname": "nth_fibonacci_number", "kind": "function", "doc": "<p>nth Fibonacci number</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>What is the 85th Fibonacci number?</td>\n  <td>$259695496911123328$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_n</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry", "modulename": "mathgenerator.geometry", "kind": "module", "doc": "<p></p>\n"}, {"fullname": "mathgenerator.geometry.angle_btw_vectors", "modulename": "mathgenerator.geometry", "qualname": "angle_btw_vectors", "kind": "function", "doc": "<p>Angle between 2 vectors</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>angle between the vectors $[363.84, 195.54, 997.08, 39.26, 60.14, 722.7, 888.57, 713.15, 436.22, 712.23, 349.23, 595.91, 191.8, 824.58, 861.56, 122.73, 815.14, 700.68, 506.5]$ and $[760.85, 934.67, 513.37, 796.93, 809.97, 423.54, 162.69, 758.96, 133.42, 478.14, 771.84, 824.88, 483.07, 134.41, 954.41, 893.42, 191.01, 453.97, 648.59]$ is:</td>\n  <td>$0.81$ radians</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_elt_amt</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.angle_regular_polygon", "modulename": "mathgenerator.geometry", "qualname": "angle_regular_polygon", "kind": "function", "doc": "<p>Angle of a Regular Polygon</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Find the angle of a regular polygon with $8$ sides</td>\n  <td>$135.0$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">min_val</span><span class=\"o\">=</span><span class=\"mi\">3</span>, </span><span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.arc_length", "modulename": "mathgenerator.geometry", "qualname": "arc_length", "kind": "function", "doc": "<p>Arc length of Angle</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Given radius, $44$ and angle, $184$. Find the arc length of the angle.</td>\n  <td>Arc length of the angle $= 141.30186$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">49</span>, </span><span class=\"param\"><span class=\"n\">max_angle</span><span class=\"o\">=</span><span class=\"mi\">359</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.area_of_circle", "modulename": "mathgenerator.geometry", "qualname": "area_of_circle", "kind": "function", "doc": "<p>Area of Circle</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Area of circle with radius $29=$</td>\n  <td>$2642.08$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.area_of_circle_given_center_and_point", "modulename": "mathgenerator.geometry", "qualname": "area_of_circle_given_center_and_point", "kind": "function", "doc": "<p>Area of Circle given center and a point on circle</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Area of circle with center $(7,-6)$ and passing through $(1.0, -6.0)$ is</td>\n  <td>$113.1$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_coordinate</span><span class=\"o\">=</span><span class=\"mi\">10</span>, </span><span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.area_of_triangle", "modulename": "mathgenerator.geometry", "qualname": "area_of_triangle", "kind": "function", "doc": "<p>Area of Triangle</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Area of triangle with side lengths: $8, 1, 8 = $</td>\n  <td>$3.99$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_a</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_b</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.basic_trigonometry", "modulename": "mathgenerator.geometry", "qualname": "basic_trigonometry", "kind": "function", "doc": "<p>Trigonometric Values</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$\\sin(30) = $</td>\n  <td>$\\frac{1}{2}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">angles</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">30</span><span class=\"p\">,</span> <span class=\"mi\">45</span><span class=\"p\">,</span> <span class=\"mi\">60</span><span class=\"p\">,</span> <span class=\"mi\">90</span><span class=\"p\">]</span>, </span><span class=\"param\"><span class=\"n\">functions</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"s1\">&#39;sin&#39;</span><span class=\"p\">,</span> <span class=\"s1\">&#39;cos&#39;</span><span class=\"p\">,</span> <span class=\"s1\">&#39;tan&#39;</span><span class=\"p\">]</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.circumference", "modulename": "mathgenerator.geometry", "qualname": "circumference", "kind": "function", "doc": "<p>Circumference of Circle</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Circumference of circle with radius $56 = $</td>\n  <td>$351.86$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.complementary_and_supplementary_angle", "modulename": "mathgenerator.geometry", "qualname": "complementary_and_supplementary_angle", "kind": "function", "doc": "<p>Complementary and Supplementary Angle</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>The complementary angle of $15 =$</td>\n  <td>$75$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_supp</span><span class=\"o\">=</span><span class=\"mi\">180</span>, </span><span class=\"param\"><span class=\"n\">max_comp</span><span class=\"o\">=</span><span class=\"mi\">90</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.curved_surface_area_cylinder", "modulename": "mathgenerator.geometry", "qualname": "curved_surface_area_cylinder", "kind": "function", "doc": "<p>Curved surface area of a cylinder</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>What is the curved surface area of a cylinder of radius, $44$ and height, $92$?</td>\n  <td>$25434.33$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">49</span>, </span><span class=\"param\"><span class=\"n\">max_height</span><span class=\"o\">=</span><span class=\"mi\">99</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.degree_to_rad", "modulename": "mathgenerator.geometry", "qualname": "degree_to_rad", "kind": "function", "doc": "<p>Degrees to Radians</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Angle $113$ degrees in radians is:</td>\n  <td>$1.97$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_deg</span><span class=\"o\">=</span><span class=\"mi\">360</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.equation_of_line_from_two_points", "modulename": "mathgenerator.geometry", "qualname": "equation_of_line_from_two_points", "kind": "function", "doc": "<p>Equation of line from two points</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>What is the equation of the line between points $(13,9)$ and $(6,-19)$ in slope-intercept form?</td>\n  <td>$y = 4x -43$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_coordinate</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">min_coordinate</span><span class=\"o\">=-</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.fourth_angle_of_quadrilateral", "modulename": "mathgenerator.geometry", "qualname": "fourth_angle_of_quadrilateral", "kind": "function", "doc": "<p>Fourth Angle of Quadrilateral</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Fourth angle of quadrilateral with angles $162 , 43, 78 =$</td>\n  <td>$77$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_angle</span><span class=\"o\">=</span><span class=\"mi\">180</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.perimeter_of_polygons", "modulename": "mathgenerator.geometry", "qualname": "perimeter_of_polygons", "kind": "function", "doc": "<p>Perimeter of Polygons</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>The perimeter of a $4$ sided polygon with lengths of $30, 105, 78, 106$cm is:</td>\n  <td>$319$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_sides</span><span class=\"o\">=</span><span class=\"mi\">12</span>, </span><span class=\"param\"><span class=\"n\">max_length</span><span class=\"o\">=</span><span class=\"mi\">120</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.pythagorean_theorem", "modulename": "mathgenerator.geometry", "qualname": "pythagorean_theorem", "kind": "function", "doc": "<p>Pythagorean Theorem</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>What is the hypotenuse of a right triangle given the other two sides have lengths $9$ and $10$?</td>\n  <td>$13.45$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_length</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.radian_to_deg", "modulename": "mathgenerator.geometry", "qualname": "radian_to_deg", "kind": "function", "doc": "<p>Radians to Degrees</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_rad</span><span class=\"o\">=</span><span class=\"mf\">6.28</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.sector_area", "modulename": "mathgenerator.geometry", "qualname": "sector_area", "kind": "function", "doc": "<p>Area of a Sector</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>What is the area of a sector with radius $42$ and angle $83$ degrees?</td>\n  <td>$1277.69$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">49</span>, </span><span class=\"param\"><span class=\"n\">max_angle</span><span class=\"o\">=</span><span class=\"mi\">359</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.sum_of_polygon_angles", "modulename": "mathgenerator.geometry", "qualname": "sum_of_polygon_angles", "kind": "function", "doc": "<p>Sum of Angles of Polygon</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>What is the sum of interior angles of a polygon with $8$ sides?</td>\n  <td>$1080$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_sides</span><span class=\"o\">=</span><span class=\"mi\">12</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.surface_area_cone", "modulename": "mathgenerator.geometry", "qualname": "surface_area_cone", "kind": "function", "doc": "<p>Surface area of a cone</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Surface area of cone with height $= 26m$ and radius $= 6m$ is</td>\n  <td>$616 m^2$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_height</span><span class=\"o\">=</span><span class=\"mi\">50</span>, </span><span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.surface_area_cube", "modulename": "mathgenerator.geometry", "qualname": "surface_area_cube", "kind": "function", "doc": "<p>Surface area of a cube</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Surface area of cube with side $= 6m$ is</td>\n  <td>$216 m^2$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_side</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.surface_area_cuboid", "modulename": "mathgenerator.geometry", "qualname": "surface_area_cuboid", "kind": "function", "doc": "<p>Surface area of a cuboid</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Surface area of cuboid with sides of lengths: $11m, 20m, 8m$ is</td>\n  <td>$936 m^2$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_side</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.surface_area_cylinder", "modulename": "mathgenerator.geometry", "qualname": "surface_area_cylinder", "kind": "function", "doc": "<p>Surface area of a cylinder</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Surface area of cylinder with height $= 26m$ and radius $= 15m$ is</td>\n  <td>$3864 m^2$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_height</span><span class=\"o\">=</span><span class=\"mi\">50</span>, </span><span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.surface_area_pyramid", "modulename": "mathgenerator.geometry", "qualname": "surface_area_pyramid", "kind": "function", "doc": "<p>Surface area of a pyramid</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Surface area of pyramid with base length $= 30m$, base width $= 40m$, and height $= 25m$ is</td>\n  <td>$2400 m^2$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.surface_area_sphere", "modulename": "mathgenerator.geometry", "qualname": "surface_area_sphere", "kind": "function", "doc": "<p>Surface area of a sphere</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Surface area of a sphere with radius $= 8m$ is</td>\n  <td>$804.25 m^2$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_side</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.third_angle_of_triangle", "modulename": "mathgenerator.geometry", "qualname": "third_angle_of_triangle", "kind": "function", "doc": "<p>Third Angle of Triangle</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Third angle of triangle with angles $10$ and $22 =$</td>\n  <td>$148$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_angle</span><span class=\"o\">=</span><span class=\"mi\">89</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.valid_triangle", "modulename": "mathgenerator.geometry", "qualname": "valid_triangle", "kind": "function", "doc": "<p>Valid Triangle</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Does triangel with sides $10, 31$ and $14$ exist?</td>\n  <td>No</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_side_length</span><span class=\"o\">=</span><span class=\"mi\">50</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.volume_cone", "modulename": "mathgenerator.geometry", "qualname": "volume_cone", "kind": "function", "doc": "<p>Volume of a cone</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Volume of cone with height $= 44m$ and radius $= 11m$ is</td>\n  <td>$5575 m^3$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_height</span><span class=\"o\">=</span><span class=\"mi\">50</span>, </span><span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.volume_cube", "modulename": "mathgenerator.geometry", "qualname": "volume_cube", "kind": "function", "doc": "<p>Volume of a cube</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Volume of a cube with a side length of $19m$ is</td>\n  <td>$6859 m^3$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_side</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.volume_cuboid", "modulename": "mathgenerator.geometry", "qualname": "volume_cuboid", "kind": "function", "doc": "<p>Volume of a cuboid</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Volume of cuboid with sides = $17m, 11m, 13m$ is</td>\n  <td>$2431 m^3$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_side</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.volume_cylinder", "modulename": "mathgenerator.geometry", "qualname": "volume_cylinder", "kind": "function", "doc": "<p>Volume of a cylinder</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Volume of cylinder with height $= 3m$ and radius $= 10m$ is</td>\n  <td>$942 m^3$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_height</span><span class=\"o\">=</span><span class=\"mi\">50</span>, </span><span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.volume_cone_frustum", "modulename": "mathgenerator.geometry", "qualname": "volume_cone_frustum", "kind": "function", "doc": "<p>Volume of the frustum of a cone</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Volume of frustum with height $= 30m$ and $r1 = 20m$ is and $r2 = 8m$ is</td>\n  <td>$19603.54 m^3$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_r1</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_r2</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_height</span><span class=\"o\">=</span><span class=\"mi\">50</span>, </span><span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.volume_hemisphere", "modulename": "mathgenerator.geometry", "qualname": "volume_hemisphere", "kind": "function", "doc": "<p>Volume of a hemisphere</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Volume of hemisphere with radius $32m =$</td>\n  <td>$68629.14 m^3$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.volume_pyramid", "modulename": "mathgenerator.geometry", "qualname": "volume_pyramid", "kind": "function", "doc": "<p>Volume of a pyramid</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Volume of pyramid with base length $= 7 m$, base width $= 18 m$ and height $= 42 m$ is</td>\n  <td>$1764.0 m^3$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_length</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_width</span><span class=\"o\">=</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_height</span><span class=\"o\">=</span><span class=\"mi\">50</span>, </span><span class=\"param\"><span class=\"n\">unit</span><span class=\"o\">=</span><span class=\"s1\">&#39;m&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.geometry.volume_sphere", "modulename": "mathgenerator.geometry", "qualname": "volume_sphere", "kind": "function", "doc": "<p>Volume of a sphere</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Volume of sphere with radius $30 m = $</td>\n  <td>$113097.36 m^3$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_radius</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc", "modulename": "mathgenerator.misc", "kind": "module", "doc": "<p></p>\n"}, {"fullname": "mathgenerator.misc.arithmetic_progression_sum", "modulename": "mathgenerator.misc", "qualname": "arithmetic_progression_sum", "kind": "function", "doc": "<p>Arithmetic Progression Sum</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Find the sum of first $44$ terms of the AP series: $49, 145, 241 ... $</td>\n  <td>$92972.0$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_d</span><span class=\"o\">=</span><span class=\"mi\">100</span>, </span><span class=\"param\"><span class=\"n\">max_a</span><span class=\"o\">=</span><span class=\"mi\">100</span>, </span><span class=\"param\"><span class=\"n\">max_n</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc.arithmetic_progression_term", "modulename": "mathgenerator.misc", "qualname": "arithmetic_progression_term", "kind": "function", "doc": "<p>Arithmetic Progression Term</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Find term number $12$ of the AP series: $-54, 24, 102 ... $</td>\n  <td>$804$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_d</span><span class=\"o\">=</span><span class=\"mi\">100</span>, </span><span class=\"param\"><span class=\"n\">max_a</span><span class=\"o\">=</span><span class=\"mi\">100</span>, </span><span class=\"param\"><span class=\"n\">max_n</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc.base_conversion", "modulename": "mathgenerator.misc", "qualname": "base_conversion", "kind": "function", "doc": "<p>Base Conversion</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Convert $45204$ from base $10$ to base $4$</td>\n  <td>$23002110$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_num</span><span class=\"o\">=</span><span class=\"mi\">60000</span>, </span><span class=\"param\"><span class=\"n\">max_base</span><span class=\"o\">=</span><span class=\"mi\">16</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc.binomial_distribution", "modulename": "mathgenerator.misc", "qualname": "binomial_distribution", "kind": "function", "doc": "<p>Binomial distribution</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>A manufacturer of metal pistons finds that, on average, $30.56$% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of $20$ pistons will contain no more than $2$ rejected pistons?</td>\n  <td>$3.17$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc.celsius_to_fahrenheit", "modulename": "mathgenerator.misc", "qualname": "celsius_to_fahrenheit", "kind": "function", "doc": "<p>Celsius to Fahrenheit</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Convert $-46$ degrees Celsius to degrees Fahrenheit</td>\n  <td>$-50.8$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_temp</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc.common_factors", "modulename": "mathgenerator.misc", "qualname": "common_factors", "kind": "function", "doc": "<p>Common Factors</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Common Factors of $100$ and $44 = $</td>\n  <td>$[1, 2, 4]$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc.complex_to_polar", "modulename": "mathgenerator.misc", "qualname": "complex_to_polar", "kind": "function", "doc": "<p>Complex to polar form</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>$19.42(-19.0\\theta + i-4.0\\theta)$</td>\n  <td>$-2.93$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">min_real_imaginary_num</span><span class=\"o\">=-</span><span class=\"mi\">20</span>, </span><span class=\"param\"><span class=\"n\">max_real_imaginary_num</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc.decimal_to_roman_numerals", "modulename": "mathgenerator.misc", "qualname": "decimal_to_roman_numerals", "kind": "function", "doc": "<p>Decimal to Roman Numerals</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>The number $92$ in roman numerals is:</td>\n  <td>$XCII$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_decimal</span><span class=\"o\">=</span><span class=\"mi\">4000</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc.euclidian_norm", "modulename": "mathgenerator.misc", "qualname": "euclidian_norm", "kind": "function", "doc": "<p>Euclidian norm or L2 norm of a vector</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Euclidian norm or L2 norm of the vector $[659.9225071540442, 243.40887829281564, 128.79950053874424, 263.19226900031344]$ is:</td>\n  <td>$761.97$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">maxEltAmt</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc.factors", "modulename": "mathgenerator.misc", "qualname": "factors", "kind": "function", "doc": "<p>Factors of a number</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Factors of $176 = $</td>\n  <td>$[1, 2, 4, 8, 11, 16, 22, 44, 88, 176]$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">1000</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc.geometric_mean", "modulename": "mathgenerator.misc", "qualname": "geometric_mean", "kind": "function", "doc": "<p>Geometric Mean of N Numbers</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Geometric mean of $3$ numbers $[72, 21, 87] = $</td>\n  <td>$50.86$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_value</span><span class=\"o\">=</span><span class=\"mi\">100</span>, </span><span class=\"param\"><span class=\"n\">max_count</span><span class=\"o\">=</span><span class=\"mi\">4</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc.geometric_progression", "modulename": "mathgenerator.misc", "qualname": "geometric_progression", "kind": "function", "doc": "<p>Geometric Progression</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>For the given GP $[11, 44, 176, 704, 2816, 11264]$. Find the value of a common ratio, 7th term value, sum upto 10th term</td>\n  <td>The value of a is $11$, common ratio is $4$ , 7th term is $45056$, sum upto 10th term is $3844775.0$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">number_values</span><span class=\"o\">=</span><span class=\"mi\">6</span>, </span><span class=\"param\"><span class=\"n\">min_value</span><span class=\"o\">=</span><span class=\"mi\">2</span>, </span><span class=\"param\"><span class=\"n\">max_value</span><span class=\"o\">=</span><span class=\"mi\">12</span>, </span><span class=\"param\"><span class=\"n\">n_term</span><span class=\"o\">=</span><span class=\"mi\">7</span>, </span><span class=\"param\"><span class=\"n\">sum_term</span><span class=\"o\">=</span><span class=\"mi\">5</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc.harmonic_mean", "modulename": "mathgenerator.misc", "qualname": "harmonic_mean", "kind": "function", "doc": "<p>Harmonic Mean of N Numbers</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Harmonic mean of $4$ numbers $52, 56, 25, 57 = $</td>\n  <td>$602.33$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_value</span><span class=\"o\">=</span><span class=\"mi\">100</span>, </span><span class=\"param\"><span class=\"n\">max_count</span><span class=\"o\">=</span><span class=\"mi\">4</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc.is_leap_year", "modulename": "mathgenerator.misc", "qualname": "is_leap_year", "kind": "function", "doc": "<p>Is Leap Year or Not</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Is $2000$ a leap year?</td>\n  <td>$2000$ is a leap year</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">minNumber</span><span class=\"o\">=</span><span class=\"mi\">1900</span>, </span><span class=\"param\"><span class=\"n\">max_number</span><span class=\"o\">=</span><span class=\"mi\">2099</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc.lcm", "modulename": "mathgenerator.misc", "qualname": "lcm", "kind": "function", "doc": "<p>LCM (Least Common Multiple)</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>LCM of $3$ and $18 = $</td>\n  <td>$18$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc.minutes_to_hours", "modulename": "mathgenerator.misc", "qualname": "minutes_to_hours", "kind": "function", "doc": "<p>Convert minutes to hours and minutes</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Convert $836$ minutes to hours &amp; minutes</td>\n  <td>$13$ hours and $56$ minutes</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_minutes</span><span class=\"o\">=</span><span class=\"mi\">999</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc.prime_factors", "modulename": "mathgenerator.misc", "qualname": "prime_factors", "kind": "function", "doc": "<p>Prime Factors</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Find prime factors of $30$</td>\n  <td>$2, 3, 5$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">min_val</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">200</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc.product_of_scientific_notations", "modulename": "mathgenerator.misc", "qualname": "product_of_scientific_notations", "kind": "function", "doc": "<p>Product of scientific notations</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Product of scientific notations $5.11 \\times 10^{67}$ and $3.64 \\times 10^{-59} = $</td>\n  <td>$1.86 \\times 10^{9}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">min_exp_val</span><span class=\"o\">=-</span><span class=\"mi\">100</span>, </span><span class=\"param\"><span class=\"n\">max_exp_val</span><span class=\"o\">=</span><span class=\"mi\">100</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc.profit_loss_percent", "modulename": "mathgenerator.misc", "qualname": "profit_loss_percent", "kind": "function", "doc": "<p>Profit or Loss Percent</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Loss percent when $CP = 751$ and $SP = 290$ is:</td>\n  <td>$61.38$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_cp</span><span class=\"o\">=</span><span class=\"mi\">1000</span>, </span><span class=\"param\"><span class=\"n\">max_sp</span><span class=\"o\">=</span><span class=\"mi\">1000</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc.quotient_of_power_same_base", "modulename": "mathgenerator.misc", "qualname": "quotient_of_power_same_base", "kind": "function", "doc": "<p>Quotient of Powers with Same Base</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>The Quotient of $5^{6}$ and $5^{8} = 5^{6-8} = 5^{-2}$</td>\n  <td>$0.04$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_base</span><span class=\"o\">=</span><span class=\"mi\">50</span>, </span><span class=\"param\"><span class=\"n\">max_power</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc.quotient_of_power_same_power", "modulename": "mathgenerator.misc", "qualname": "quotient_of_power_same_power", "kind": "function", "doc": "<p>Quotient of Powers with Same Power</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>The quotient of $19^{8}$ and $10^{8} = (19/10)^8 = 1.9^{8}$</td>\n  <td>$169.84$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_base</span><span class=\"o\">=</span><span class=\"mi\">50</span>, </span><span class=\"param\"><span class=\"n\">max_power</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc.set_operation", "modulename": "mathgenerator.misc", "qualname": "set_operation", "kind": "function", "doc": "<p>Union, Intersection, Difference of Two Sets</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Given the two sets $a={1, 2, 4, 5}$, $b={8, 1, 2}$. Find the Union, intersection, $a-b$, $b-a$, and symmetric difference</td>\n  <td>Union is ${1, 2, 4, 5, 8}$. Intersection is ${1, 2}$, $a-b$ is ${4, 5}$, $b-a$ is ${8}$. Symmetric difference is ${4, 5, 8}$.</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">min_size</span><span class=\"o\">=</span><span class=\"mi\">3</span>, </span><span class=\"param\"><span class=\"n\">max_size</span><span class=\"o\">=</span><span class=\"mi\">7</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc.signum_function", "modulename": "mathgenerator.misc", "qualname": "signum_function", "kind": "function", "doc": "<p>Signum Function</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Signum of $-229$ is =</td>\n  <td>$-1$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"nb\">min</span><span class=\"o\">=-</span><span class=\"mi\">999</span>, </span><span class=\"param\"><span class=\"nb\">max</span><span class=\"o\">=</span><span class=\"mi\">999</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.misc.surds_comparison", "modulename": "mathgenerator.misc", "qualname": "surds_comparison", "kind": "function", "doc": "<p>Comparing Surds</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Fill in the blanks $42^{\\frac{1}{2}}$ _ $45^{\\frac{1}{5}}$</td>\n  <td>$&gt;$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_value</span><span class=\"o\">=</span><span class=\"mi\">100</span>, </span><span class=\"param\"><span class=\"n\">max_root</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.statistics", "modulename": "mathgenerator.statistics", "kind": "module", "doc": "<p></p>\n"}, {"fullname": "mathgenerator.statistics.combinations", "modulename": "mathgenerator.statistics", "qualname": "combinations", "kind": "function", "doc": "<p>Combinations of Objects</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Find the number of combinations from $19$ objects picked $6$ at a time.</td>\n  <td>$27132$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_lengthgth</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.statistics.conditional_probability", "modulename": "mathgenerator.statistics", "qualname": "conditional_probability", "kind": "function", "doc": "<p>Conditional Probability</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Someone tested positive for a nasty disease which only $1.18$% of the population have. Test sensitivity (true positive) is equal to $SN=98.73$% whereas test specificity (true negative) $SP=99.99$%. What is the probability that this guy really has that disease?</td>\n  <td>$99.16$%</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.statistics.confidence_interval", "modulename": "mathgenerator.statistics", "qualname": "confidence_interval", "kind": "function", "doc": "<p>Confidence interval For sample S</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>The confidence interval for sample $[234, 223, 210, 203, 258, 299, 281, 208, 278, 252, 295, 245, 280, 235, 219, 297, 214, 267, 212, 256, 232, 221]$ with $99$% confidence is</td>\n  <td>$(263.31, 229.33)$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.statistics.data_summary", "modulename": "mathgenerator.statistics", "qualname": "data_summary", "kind": "function", "doc": "<p>Mean, Standard Deviation and Variance</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Find the mean,standard deviation and variance for the data $9, 29, 46, 27, 46, 15, 10, 44, 19, 33, 38, 7, 34, 28, 8$</td>\n  <td>The Mean is $26.2$, Standard Deviation is $186.29$, Variance is $13.65$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">number_values</span><span class=\"o\">=</span><span class=\"mi\">15</span>, </span><span class=\"param\"><span class=\"n\">min_val</span><span class=\"o\">=</span><span class=\"mi\">5</span>, </span><span class=\"param\"><span class=\"n\">max_val</span><span class=\"o\">=</span><span class=\"mi\">50</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.statistics.dice_sum_probability", "modulename": "mathgenerator.statistics", "qualname": "dice_sum_probability", "kind": "function", "doc": "<p>Probability of a certain sum appearing on faces of dice</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>If $2$ dice are rolled at the same time, the probability of getting a sum of $5 =$</td>\n  <td>$\\frac{4}{36}$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_dice</span><span class=\"o\">=</span><span class=\"mi\">3</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.statistics.mean_median", "modulename": "mathgenerator.statistics", "qualname": "mean_median", "kind": "function", "doc": "<p>Mean and Median</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Given the series of numbers $[4, 19, 21, 22, 43, 44, 60, 81, 87, 92]$. Find the arithmatic mean and median of the series</td>\n  <td>Arithmetic mean of the series is $47.3$ and arithmetic median of this series is $43.5$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_length</span><span class=\"o\">=</span><span class=\"mi\">10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, {"fullname": "mathgenerator.statistics.permutation", "modulename": "mathgenerator.statistics", "qualname": "permutation", "kind": "function", "doc": "<p>Permutations</p>\n\n<table>\n<thead>\n<tr>\n  <th>Ex. Problem</th>\n  <th>Ex. Solution</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n  <td>Number of Permutations from $18$ objects picked $5$ at a time is:</td>\n  <td>$1028160$</td>\n</tr>\n</tbody>\n</table>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">max_lengthgth</span><span class=\"o\">=</span><span class=\"mi\">20</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}];
 
     // mirrored in build-search-index.js (part 1)
     // Also split on html tags. this is a cheap heuristic, but good enough.
diff --git a/mathgenerator/algebra.py b/mathgenerator/algebra.py
index 5120ee7..0b6b839 100644
--- a/mathgenerator/algebra.py
+++ b/mathgenerator/algebra.py
@@ -65,7 +65,7 @@ def complex_quadratic(prob_type=0, max_range=10):
 
     | Ex. Problem | Ex. Solution |
     | --- | --- |
-    | Find the roots of given Quadratic Equation $x^2 + 8x + 8 = 0$ | $((-1.172, -6.828)) = (\frac{-8 + \sqrt{32}}{2*1}, (\frac{-8 - \sqrt{32}}{2*1})$ |
+    | Find the roots of given Quadratic Equation $x^2 + 8x + 8 = 0$ | $((-1.172, -6.828)) = (\frac{-8 + \sqrt{32}}{2}, (\frac{-8 - \sqrt{32}}{2})$ |
     """
     if prob_type < 0 or prob_type > 1:
         print("prob_type not supported")
@@ -110,9 +110,9 @@ def complex_quadratic(prob_type=0, max_range=10):
 
         if sqrt_d - int(sqrt_d) == 0:
             sqrt_d = int(sqrt_d)
-            solution = rf'(\frac{{{-b} + {sqrt_d}i}}{{2*{a}}}, \frac{{{-b} - {sqrt_d}i}}{{2*{a}}})'
+            solution = rf'(\frac{{{-b} + {sqrt_d}i}}{{{2*a}}}, \frac{{{-b} - {sqrt_d}i}}{{{2*a}}})'
         else:
-            solution = rf'(\frac{{{-b} + \sqrt{{{-d}}}i}}{{2*{a}}}, \frac{{{-b} - \sqrt{{{-d}}}i}}{{2*{a}}})'
+            solution = rf'(\frac{{{-b} + \sqrt{{{-d}}}i}}{{{2*a}}}, \frac{{{-b} - \sqrt{{{-d}}}i}}{{{2*a}}})'
 
         return problem, solution
 
@@ -124,9 +124,9 @@ def complex_quadratic(prob_type=0, max_range=10):
 
         if sqrt_d - int(sqrt_d) == 0:
             sqrt_d = int(sqrt_d)
-            g_sol = rf'(\frac{{{-b} + {sqrt_d}}}{{2*{a}}}, \frac{{{-b} - {sqrt_d}}}{{2*{a}}})'
+            g_sol = rf'(\frac{{{-b} + {sqrt_d}}}{{{2*a}}}, \frac{{{-b} - {sqrt_d}}}{{{2*a}}})'
         else:
-            g_sol = rf'(\frac{{{-b} + \sqrt{{{d}}}}}{{2*{a}}}, (\frac{{{-b} - \sqrt{{{d}}}}}{{2*{a}}})'
+            g_sol = rf'(\frac{{{-b} + \sqrt{{{d}}}}}{{{2*a}}}, (\frac{{{-b} - \sqrt{{{d}}}}}{{{2*a}}})'
 
         solution = f'$({s_root1, s_root2}) = {g_sol}$'
 
diff --git a/mathgenerator/basic_math.py b/mathgenerator/basic_math.py
index 1716f98..b6f9622 100644
--- a/mathgenerator/basic_math.py
+++ b/mathgenerator/basic_math.py
@@ -6,7 +6,7 @@ def absolute_difference(max_a=100, max_b=100):
 
     | Ex. Problem | Ex. Solution |
     | --- | --- |
-    | $|22-34|=$ | $12$ |
+    | $\|22-34\|=$ | $12$ |
     """
     a = random.randint(-1 * max_a, max_a)
     b = random.randint(-1 * max_b, max_b)
diff --git a/mathgenerator/calculus.py b/mathgenerator/calculus.py
index 9c83591..0455d7d 100644
--- a/mathgenerator/calculus.py
+++ b/mathgenerator/calculus.py
@@ -83,7 +83,7 @@ def stationary_points(max_exp=3, max_coef=10):
 
     | Ex. Problem | Ex. Solution |
     | --- | --- |
-    | $f(x)=6*x^3 + 6*x^2 + x + 8$ | ${- \frac{1}{3} - \frac{\sqrt{2}}{6}, - \frac{1}{3} + \frac{\sqrt{2}}{6}}$ |
+    | $f(x)=6x^3 + 6x^2 + x + 8$ | ${- \frac{1}{3} - \frac{\sqrt{2}}{6}, - \frac{1}{3} + \frac{\sqrt{2}}{6}}$ |
     """
     solution = ''
     while len(solution) == 0:
@@ -94,7 +94,7 @@ def stationary_points(max_exp=3, max_coef=10):
             problem += coefficient * pow(x, exp)
         solution = sympy.stationary_points(problem, x)
 
-    problem = 'f(x)=' + str(problem).replace('**', '^')
+    problem = 'f(x)=' + str(problem).replace('**', '^').replace('*','')
     return f'${problem}$', f'${sympy.latex(solution)[6:-8]}}}$'
 
 
diff --git a/mathgenerator/geometry.py b/mathgenerator/geometry.py
index 815341e..a36dee9 100644
--- a/mathgenerator/geometry.py
+++ b/mathgenerator/geometry.py
@@ -554,6 +554,7 @@ def volume_cone(max_radius=20, max_height=50, unit='m'):
 
 def volume_cube(max_side=20, unit='m'):
     """Volume of a cube
+    
     | Ex. Problem | Ex. Solution |
     | --- | --- |
     | Volume of a cube with a side length of $19m$ is | $6859 m^3$ |
diff --git a/mathgenerator/misc.py b/mathgenerator/misc.py
index 4306872..a88a314 100644
--- a/mathgenerator/misc.py
+++ b/mathgenerator/misc.py
@@ -476,7 +476,7 @@ def quotient_of_power_same_base(max_base=50, max_power=10):
 
     | Ex. Problem | Ex. Solution |
     | --- | --- |
-    | The Quotient of $5^{6}$ and $5^{8} = $5^{6-8} = 5^{-2}$ | $0.04$ |
+    | The Quotient of $5^{6}$ and $5^{8} = 5^{6-8} = 5^{-2}$ | $0.04$ |
     """
     base = random.randint(1, max_base)
     power1 = random.randint(1, max_power)
@@ -485,7 +485,7 @@ def quotient_of_power_same_base(max_base=50, max_power=10):
     solution = base ** step
 
     problem = f"The Quotient of ${base}^{{{power1}}}$ and ${base}^{{{power2}}} = " \
-        f"${base}^{{{power1}-{power2}}} = {base}^{{{step}}}$"
+        f"{base}^{{{power1}-{power2}}} = {base}^{{{step}}}$"
     return problem, f'${solution}$'
 
 
@@ -512,7 +512,7 @@ def set_operation(min_size=3, max_size=7):
 
     | Ex. Problem | Ex. Solution |
     | --- | --- |
-    | Given the two sets $a={1, 2, 4, 5}$, $b={8, 1, 2}. Find the Union, intersection, a-b, b-a, and symmetric difference | Union is ${1, 2, 4, 5, 8}$. Intersection is ${1, 2}$, a-b is ${4, 5}$, b-a is ${8}$. Symmetric difference is ${4, 5, 8}$. |
+    | Given the two sets $a={1, 2, 4, 5}$, $b={8, 1, 2}$. Find the Union, intersection, $a-b$, $b-a$, and symmetric difference | Union is ${1, 2, 4, 5, 8}$. Intersection is ${1, 2}$, $a-b$ is ${4, 5}$, $b-a$ is ${8}$. Symmetric difference is ${4, 5, 8}$. |
     """
     number_variables_a = random.randint(min_size, max_size)
     number_variables_b = random.randint(min_size, max_size)
@@ -525,10 +525,10 @@ def set_operation(min_size=3, max_size=7):
     a = set(a)
     b = set(b)
 
-    problem = f"Given the two sets $a={a}$, $b={b}. " + \
-        "Find the Union, intersection, a-b, b-a, and symmetric difference"
+    problem = f"Given the two sets $a={a}$, $b={b}$. " + \
+        "Find the Union, intersection, $a-b$, $b-a$, and symmetric difference"
     solution = f"Union is ${a.union(b)}$. Intersection is ${a.intersection(b)}$" + \
-        f", a-b is ${a.difference(b)}$, b-a is ${b.difference(a)}$." + \
+        f", $a-b$ is ${a.difference(b)}$, $b-a$ is ${b.difference(a)}$." + \
         f" Symmetric difference is ${a.symmetric_difference(b)}$."
     return problem, solution
 
diff --git a/mathgenerator/statistics.py b/mathgenerator/statistics.py
index f0eba4e..a598fa6 100644
--- a/mathgenerator/statistics.py
+++ b/mathgenerator/statistics.py
@@ -116,7 +116,7 @@ def data_summary(number_values=15, min_val=5, max_val=50):
 
 
 def dice_sum_probability(max_dice=3):
-    """Probability of a certain sum appearing on faces of dice
+    r"""Probability of a certain sum appearing on faces of dice
 
     | Ex. Problem | Ex. Solution |
     | --- | --- |
