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docs:More (and prettier) examples.
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‎docs/Basic-usage.ipynb‎

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},
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"cell_type": "code",
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},
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{
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"cell_type": "code",
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"metadata": {},
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"[\"Root\",[\"Add\",[\"Add\",[\"Multiply\",4,[\"Power\",\"x\",2]],[\"Multiply\",12,\"x\"]],9],2]"
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]
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{
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"cell_type": "code",
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"<table border=\"1\"><thead><tr><th>expr</th><th>Cortex-JS</th><th>LaTeX::Grammar</th></tr></thead><tbody><tr><td align=left>4 x^2 + 12 x + 9</td><td align=left>$[&quot;Add&quot;, [&quot;Multiply&quot;, 4, [&quot;Power&quot;, &quot;x&quot;, 2]], [&quot;Multiply&quot;, 12, &quot;x&quot;], 9]</td><td align=left>[&quot;Add&quot;,[&quot;Add&quot;,[&quot;Power&quot;,&quot;4 x&quot;,2],&quot;12 x&quot;],9]</td></tr><tr><td align=left>4 \\times x^2 + 12 \\times x + 9</td><td align=left>$[&quot;Add&quot;, [&quot;Multiply&quot;, 4, [&quot;Power&quot;, &quot;x&quot;, 2]], [&quot;Multiply&quot;, 12, &quot;x&quot;], 9]</td><td align=left>[&quot;Add&quot;,[&quot;Add&quot;,[&quot;Multiply&quot;,4,[&quot;Power&quot;,&quot;x&quot;,2]],[&quot;Multiply&quot;,12,&quot;x&quot;]],9]</td></tr><tr><td align=left>4 * x^2 + 12 * x + 9</td><td align=left>$[&quot;Add&quot;, [&quot;Multiply&quot;, 4, [&quot;Power&quot;, &quot;x&quot;, 2]], [&quot;Multiply&quot;, 12, &quot;x&quot;], 9]</td><td align=left>[&quot;Add&quot;,[&quot;Add&quot;,[&quot;Multiply&quot;,4,[&quot;Power&quot;,&quot;x&quot;,2]],[&quot;Multiply&quot;,12,&quot;x&quot;]],9]</td></tr><tr><td align=left>\\sqrt{4 * x^2 + 12 * x + 9}</td><td align=left>$[&quot;Sqrt&quot;, [&quot;Add&quot;, [&quot;Multiply&quot;, 4, [&quot;Power&quot;, &quot;x&quot;, 2]], [&quot;Multiply&quot;, 12, &quot;x&quot;], 9]]</td><td align=left>[&quot;Root&quot;,[&quot;Add&quot;,[&quot;Add&quot;,[&quot;Multiply&quot;,4,[&quot;Power&quot;,&quot;x&quot;,2]],[&quot;Multiply&quot;,12,&quot;x&quot;]],9],2]</td></tr></tbody></table>"
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"-1"
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},
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"cell_type": "code",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"a^2+b^2+2ab"
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"$a^2+b^2+2ab$"
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]
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},
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"metadata": {},
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},
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"data": {
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"2x^2+3x^2+x+5 = 5x^2+x+5"
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"text/markdown": [
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"$2x^2+3x^2+x+5$ = $5x^2+x+5$"
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]
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},
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"metadata": {},
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],
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"source": [
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"#%markdown\n",
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"my $expr = parse-latex('3x^2 + 2x^2 + x + 5');\n",
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"\"{to-latex($expr)} = {to-latex(simplify($expr))}\";"
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"text/markdown": [
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"$$\n",
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"\\sqrt{5x^2+x+5}\n",
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"$$"
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"$\\sqrt{5x^2+x+5}$"
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]
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"'\\sqrt{3x^2 + 2x^2 + x + 5}'\n",
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"==> parse-latex()\n",
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"==> simplify()\n",
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"==> to-latex()\n",
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"==> { $_.subst(/ '\\text{\\text{' (.*) '}}' $ /, {$0.Str}) }()\n",
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"==> { \"\\$\\$\\n$_\\n\\$\\$\" }()"
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"==> to-latex()"
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]
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},
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{
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"cell_type": "markdown",
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"id": "63c7bf3d",
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"metadata": {},
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"source": [
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"----\n",
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"\n",
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"## Solve equations"
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]
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},
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"cell_type": "code",
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"id": "de5cb448",
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"metadata": {},
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"outputs": [
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"data": {
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"text/plain": [
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"[3 2]"
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]
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},
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"execution_count": 29,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"'x^2 - 5 x + 6 = 0'\n",
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"==> parse-latex() \n",
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"==> solve()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 30,
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"id": "d1b1cc90",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/markdown": [
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"$3+2\\sqrt{2}, \\: 3-2\\sqrt{2}$"
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]
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},
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"execution_count": 30,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"#%markdown\n",
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"'x^2 - 6 x + 1 = 0'\n",
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"==> parse-latex() \n",
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"==> solve()\n",
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"==> to-latex()"
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]
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},
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"cell_type": "code",
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"id": "2d11e132",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/markdown": [
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"$x+\\frac{1}{x}$"
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]
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},
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"execution_count": 31,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"#% markdown\n",
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"'x^2 - a x + 1 = 0'\n",
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"==> parse-latex() \n",
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"==> solve(vars => 'a')\n",
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"==> to-latex()"
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]
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},
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{
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"cell_type": "markdown",
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"id": "42ba6296",
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"metadata": {},
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"source": [
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"---\n",
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"\n",
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"## Calculus"
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]
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},
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"id": "5bde1c7c",
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"metadata": {},
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"outputs": [
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"data": {
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"text/markdown": [
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"$2x$"
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]
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},
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"#%markdown\n",
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"'D_x (x^2 + 1)'\n",
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"==> parse-latex()\n",
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"==> evaluate()\n",
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"==> to-latex()"
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]
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},
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"cell_type": "code",
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"id": "9ee1cb09",
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"metadata": {},
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"outputs": [
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"data": {
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"text/markdown": [
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"$\\frac{x^3}{3}$"
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]
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},
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"execution_count": 33,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"#%markdown\n",
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"'\\int x^2 dx'\n",
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"==> parse-latex()\n",
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"==> evaluate()\n",
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"==> to-latex()"
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]
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},
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"cell_type": "code",
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"data": {
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"text/markdown": [
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"$\\frac{1}{3}$"
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]
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"#%markdown\n",
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"'\\int_{0}^{1} x^2 dx'\n",
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"==> parse-latex()\n",
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"==> evaluate()\n",
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"==> to-latex()"
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"6"
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