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Artificial_Calc_Teacher_v1.8.ipynb
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{
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"cells": [
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{
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"cell_type": "raw",
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"id": "8c69730d",
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"metadata": {},
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"source": [
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"---\n",
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"title: Artificial Calculus Teacher\n",
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"description: Generates Derivative and Integral Expressions\n",
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"show-code : False\n",
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"---"
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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": 1,
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"id": "c5197005",
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"metadata": {},
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"outputs": [],
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"source": [
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"# changelog: removes custom_ln cause i don't like it"
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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": 2,
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"id": "108761f9",
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"metadata": {
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"scrolled": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Solve\n"
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]
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},
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{
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"data": {
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"text/latex": [
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"$\\displaystyle \\frac{d}{d x} x^{3} \\tan{\\left(x \\right)}$"
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],
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"text/plain": [
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"Derivative(x**3*tan(x), x)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$\\displaystyle \\int \\left(\\sqrt[3]{x} - e^{x}\\right)\\, dx$"
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],
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"text/plain": [
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"Integral(x**(1/3) - exp(x), x)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"Solutions:\n"
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]
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},
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{
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"data": {
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"text/latex": [
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"$\\displaystyle \\frac{d}{d x} x^{3} \\tan{\\left(x \\right)} = x^{3} \\sec^{2}{\\left(x \\right)} + 3 x^{2} \\tan{\\left(x \\right)}$"
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],
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"text/plain": [
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"Eq(Derivative(x**3*tan(x), x), x**3*sec(x)**2 + 3*x**2*tan(x))"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$\\displaystyle \\int \\left(\\sqrt[3]{x} - e^{x}\\right)\\, dx = \\frac{3 x^{\\frac{4}{3}}}{4} - e^{x}$"
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],
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"text/plain": [
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"Eq(Integral(x**(1/3) - exp(x), x), 3*x**(4/3)/4 - exp(x))"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"-----------------------------------------------------------------------------------------------------------\n"
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]
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}
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],
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"source": [
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"from sympy.simplify.fu import TR22\n",
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"from sympy import sin,cos,ln,exp,tan,Function,Derivative,Eq,Integral,Rational\n",
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"from sympy import factor_terms,simplify, sqrt, cbrt\n",
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"from sympy.abc import x\n",
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"import random\n",
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"f = Function('f')\n",
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"g = Function('g')\n",
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"h = Function('h')\n",
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"def random_math(x):\n",
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" allowed_values = list(range(2, 6))\n",
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" random_value = random.choice(allowed_values)\n",
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" random_value\n",
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" def power_function(x): \n",
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" return x**random_value\n",
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" def scalar_function(x):\n",
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" return x*random_value\n",
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" def addSUBTR_function(x): \n",
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" return x+random_value\n",
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" funs = [sin,power_function,ln,exp,cos,tan,sqrt,cbrt,\n",
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" scalar_function,addSUBTR_function] \n",
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" operations = [f(g(x)),f(x)+g(x),f(x)-g(x),f(x)/g(x),f(x)*g(x), f(x)/g(x)/h(x),f(x)*g(h(x)),\n",
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" f(g(h(x))),f(h(x))+g(x),f(h(x))-g(x),f(h(x))/g(x),f(x)/g(h(x)),f(h(x))*g(x), f(x)*g(x)*h(x)]\n",
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" operation = operations[random.randrange(0,len(operations))]\n",
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" return [[[operation.replace(f, i) for i in funs][random.randrange(0,len(funs))].replace(g, i) for i in funs]\\\n",
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"[random.randrange(0,len(funs))].replace(h, i) for i in funs][random.randrange(0,len(funs))]\n",
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"\n",
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"def random_math2(x):\n",
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" allowed_values = list(range(2, 6))\n",
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" random_value = random.choice(allowed_values)\n",
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" random_value\n",
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" def power_function(x): \n",
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" return x**random_value\n",
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" def scalar_function(x):\n",
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" return x*random_value\n",
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" def addSUBTR_function(x): \n",
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" return x+random_value\n",
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" funs = [sin,power_function,ln,exp,cos,tan,sqrt,cbrt,\n",
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" scalar_function,addSUBTR_function] \n",
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" operations = [f(g(x)),f(x)+g(x),f(x)-g(x),f(x)/g(x),f(x)*g(x)]\n",
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" operation = operations[random.randrange(0,len(operations))]\n",
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" return [[operation.replace(f, i) for i in funs][random.randrange(0,len(funs))].replace(g, i) for i in funs]\\\n",
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"[random.randrange(0,len(funs))]\n",
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"setup1 = random_math(x)\n",
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"setup2 = random_math2(x)\n",
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"practice1 = Derivative(simplify(setup1),x)\n",
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"practice2 = Integral(simplify(setup2),x)\n",
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"p1eq = Eq(practice1,practice1.doit(),evaluate=False)\n",
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"p2eq = Eq(practice2,practice2.doit().simplify(),evaluate=False)\n",
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"print(\"Solve\")\n",
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"display(p1eq.lhs)\n",
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"if str(factor_terms(p2eq.lhs)) != str(p2eq.rhs): \n",
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" if str(p2eq).find(\"Ei\") == -1 and str(p2eq).find(\"gamma\") == -1 and str(p2eq).find(\"Piecewise\") == -1\\\n",
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" and str(p2eq).find(\"li\") == -1 and str(p2eq).find(\"erf\") == -1 and str(p2eq).find(\"atan\") == -1\\\n",
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" and str(p2eq).find(\"Si\") == -1 and str(p2eq).find(\"Ci\") == -1 and str(p2eq).find(\"hyper\") == -1\\\n",
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" and str(p2eq).find(\"fresnel\") == -1 and str(p2eq).find(\"Li\") == -1: \n",
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" display(p2eq.lhs)\n",
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" else:\n",
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" print(\"Error: Complex Integral\")\n",
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" pass\n",
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"\n",
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"else:\n",
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" print(\"Error: Impossible Integral\") \n",
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" pass\n",
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" \n",
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"for i in range(0,8):\n",
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" print(\"\\n\")\n",
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"print(\"Solutions:\")\n",
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"display(TR22(p1eq))\n",
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"display(TR22(p2eq))\n",
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"print(\"-----------------------------------------------------------------------------------------------------------\")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "b3f5b9fb",
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"metadata": {},
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"source": [
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"If LaTeX display breaks, refresh the page.\n",
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"\n",
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"Helpful resources: https://www.derivative-calculator.net/ & https://www.integral-calculator.com/ \n",
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"\n",
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"**Made by github.com/nsc9 - MIT License**\n",
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"\n",
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"Donate by sending Bitcoin (BTC) to address: **bc1qtawr2gw52ftufzu0r3r20pnj3vmynssxs0mjl4**"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.10"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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