Update app.py

app.py

@@ -1,64 +1,142 @@
 import gradio as gr
-import json
 import random
-import math
+import json
+import tempfile
+import os
+from datetime import datetime
 
-# Define a list of topics with specific formulas and question templates
+# Define a comprehensive list of calculus topics based on James Stewart's textbook
 TOPICS = {
+    "Limits and Continuity": {
+        "formula": "For a function $f(x)$, $\\lim_{x \\to a} f(x) = L$",
+        "functions": {
+            "easy": [
+                {"func": "$\\lim_{x \\to 2} (3x+4)$", "domain": ["$x \\to 2$"], "solution": "$10$"},
+                {"func": "$\\lim_{x \\to 0} \\frac{\\sin(x)}{x}$", "domain": ["$x \\to 0$"], "solution": "$1$"},
+                {"func": "$\\lim_{x \\to 3} (x^2-5x+2)$", "domain": ["$x \\to 3$"], "solution": "$-4$"},
+                {"func": "$\\lim_{x \\to 1} \\frac{x^2-1}{x-1}$", "domain": ["$x \\to 1$"], "solution": "$2$"},
+                {"func": "$\\lim_{x \\to \\infty} \\frac{2x^2+3x-5}{x^2}$", "domain": ["$x \\to \\infty$"], "solution": "$2$"}
+            ],
+            "hard": [
+                {"func": "$\\lim_{x \\to 0} \\frac{1-\\cos(x)}{x^2}$", "domain": ["$x \\to 0$"], "solution": "$\\frac{1}{2}$"},
+                {"func": "$\\lim_{x \\to 0} (\\frac{1}{x} - \\frac{1}{\\sin(x)})$", "domain": ["$x \\to 0$"], "solution": "$0$"},
+                {"func": "$\\lim_{x \\to 0} \\frac{e^x-1-x}{x^2}$", "domain": ["$x \\to 0$"], "solution": "$\\frac{1}{2}$"},
+                {"func": "$\\lim_{x \\to \\infty} (1 + \\frac{1}{x})^x$", "domain": ["$x \\to \\infty$"], "solution": "$e$"},
+                {"func": "$\\lim_{x \\to 0^+} x^{\\alpha}\\ln(x)$ where $\\alpha > 0$", "domain": ["$x \\to 0^+$"], "solution": "$0$"}
+            ]
+        }
+    },
+    "Derivatives and Differentiation": {
+        "formula": "$f'(x) = \\lim_{h \\to 0} \\frac{f(x+h) - f(x)}{h}$",
+        "functions": {
+            "easy": [
+                {"func": "$f(x) = x^3 - 4x^2 + 7x - 2$", "domain": ["Find $f'(x)$"], "solution": "$f'(x) = 3x^2 - 8x + 7$"},
+                {"func": "$f(x) = \\sin(2x)$", "domain": ["Find $f'(x)$"], "solution": "$f'(x) = 2\\cos(2x)$"},
+                {"func": "$f(x) = e^{3x}$", "domain": ["Find $f'(x)$"], "solution": "$f'(x) = 3e^{3x}$"},
+                {"func": "$f(x) = \\ln(x^2 + 1)$", "domain": ["Find $f'(x)$"], "solution": "$f'(x) = \\frac{2x}{x^2+1}$"},
+                {"func": "$f(x) = x^2 e^x$", "domain": ["Find $f'(x)$"], "solution": "$f'(x) = x^2 e^x + 2x e^x$"}
+            ],
+            "hard": [
+                {"func": "$f(x) = \\frac{\\sin(x)}{\\cos(x) + 2}$", "domain": ["Find $f'(x)$"], "solution": "$f'(x) = \\frac{\\cos(x)(\\cos(x) + 2) + \\sin^2(x)}{(\\cos(x) + 2)^2}$"},
+                {"func": "$f(x) = \\int_{0}^{x^2} \\sin(t^2) dt$", "domain": ["Find $f'(x)$"], "solution": "$f'(x) = 2x\\sin(x^4)$"},
+                {"func": "$f(x) = \\arctan(e^x)$", "domain": ["Find $f'(x)$"], "solution": "$f'(x) = \\frac{e^x}{1 + e^{2x}}$"},
+                {"func": "$f(x) = x^{\\sin(x)}$", "domain": ["Find $f'(x)$"], "solution": "$f'(x) = x^{\\sin(x)}(\\cos(x)\\ln(x) + \\frac{\\sin(x)}{x})$"},
+                {"func": "$f(x) = \\ln(\\sin(x))$", "domain": ["Find $f'(x)$"], "solution": "$f'(x) = \\cot(x)$"}
+            ]
+        }
+    },
+    "Applications of Derivatives": {
+        "formula": "Related Rates, Optimization, L'Hôpital's Rule",
+        "functions": {
+            "easy": [
+                {"func": "A particle moves according to $s(t) = t^3 - 6t^2 + 9t$. Find its velocity at $t = 2$", "domain": ["$t = 2$"], "solution": "$v(2) = -3$ units/sec"},
+                {"func": "Find the critical points of $f(x) = x^3 - 3x^2 - 9x + 5$", "domain": ["$x \\in \\mathbb{R}$"], "solution": "$x = -1$ and $x = 3$"},
+                {"func": "Find the absolute maximum and minimum of $f(x) = x^2 - 4x + 3$ on $[0, 3]$", "domain": ["$[0, 3]$"], "solution": "Maximum: $f(0) = 3$, Minimum: $f(2) = -1$"},
+                {"func": "Use L'Hôpital's Rule to evaluate $\\lim_{x \\to 0} \\frac{\\tan(3x)}{x}$", "domain": ["$x \\to 0$"], "solution": "$3$"},
+                {"func": "Find the equation of the tangent line to $f(x) = x^2 + 2x - 3$ at $x = 1$", "domain": ["$x = 1$"], "solution": "$y = 4x - 2$"}
+            ],
+            "hard": [
+                {"func": "A ladder 10 feet long leans against a wall. If the bottom slides away at 2 ft/s, how fast is the top sliding down when it's 6 feet above ground?", "domain": ["Rate problem"], "solution": "$\\frac{3}{2}$ ft/s"},
+                {"func": "Find the dimensions of the rectangle with perimeter 100 m that has the maximum area", "domain": ["Optimization"], "solution": "25 m × 25 m square"},
+                {"func": "Use Newton's method to approximate a root of $f(x) = x^3 - 2x - 5$ starting with $x_1 = 2$", "domain": ["Newton's Method"], "solution": "$x \\approx 2.0946$ after 3 iterations"},
+                {"func": "Find the absolute extrema of $f(x) = xe^{-x^2}$ on $[0, \\infty)$", "domain": ["$[0, \\infty)$"], "solution": "Maximum: $f(\\frac{1}{\\sqrt{2}}) = \\frac{1}{\\sqrt{2e}}$, Minimum: $f(0) = f(\\infty) = 0$"},
+                {"func": "Use implicit differentiation to find $\\frac{dy}{dx}$ for $x^3 + y^3 = 6xy$", "domain": ["Implicit"], "solution": "$\\frac{dy}{dx} = \\frac{6y - 3x^2}{3y^2 - 6x}$"}
+            ]
+        }
+    },
+    "Integration Techniques": {
+        "formula": "$\\int f(x) dx$ using various methods",
+        "functions": {
+            "easy": [
+                {"func": "$\\int x^3(x^2+1)^4 dx$", "domain": ["Use Substitution"], "solution": "$\\frac{1}{10}(x^2+1)^5 - \\frac{1}{6}(x^2+1)^3 + C$"},
+                {"func": "$\\int \\frac{1}{x^2-4} dx$", "domain": ["Use Partial Fractions"], "solution": "$\\frac{1}{4}\\ln|\\frac{x-2}{x+2}| + C$"},
+                {"func": "$\\int x\\sin(x) dx$", "domain": ["Use Integration by Parts"], "solution": "$\\sin(x) - x\\cos(x) + C$"},
+                {"func": "$\\int \\sec^2(3x) dx$", "domain": ["Trigonometric"], "solution": "$\\frac{1}{3}\\tan(3x) + C$"},
+                {"func": "$\\int \\frac{5}{3x+6} dx$", "domain": ["Substitution"], "solution": "$\\frac{5}{3}\\ln|3x+6| + C$"}
+            ],
+            "hard": [
+                {"func": "$\\int \\frac{x^2}{\\sqrt{1-x^2}} dx$", "domain": ["Trigonometric Substitution"], "solution": "$-\\frac{x\\sqrt{1-x^2}}{2} - \\frac{\\arcsin(x)}{2} + C$"},
+                {"func": "$\\int \\frac{\\ln(x)}{x^2} dx$", "domain": ["Integration by Parts"], "solution": "$-\\frac{\\ln(x)}{x} - \\frac{1}{x} + C$"},
+                {"func": "$\\int e^x\\sin(x) dx$", "domain": ["Integration by Parts twice"], "solution": "$\\frac{e^x(\\sin(x)-\\cos(x))}{2} + C$"},
+                {"func": "$\\int \\frac{1}{x^2-x-6} dx$", "domain": ["Partial Fractions"], "solution": "$\\frac{1}{5}\\ln|\\frac{x+2}{x-3}| + C$"},
+                {"func": "$\\int \\frac{1}{\\sqrt{x^2-a^2}} dx$", "domain": ["$a > 0$"], "solution": "$\\ln|x + \\sqrt{x^2-a^2}| + C$"}
+            ]
+        }
+    },
     "Average Value": {
-        "formula": "f_avg = (1/(b-a)) * ∫[a,b] f(x) dx",
+        "formula": "$f_{avg} = \\frac{1}{b-a} \\int_{a}^{b} f(x) dx$",
         "functions": {
             "easy": [
-                {"func": "x^2", "domain": [0, 2], "solution": "4/3"},
-                {"func": "sin(x)", "domain": [0, "π"], "solution": "2/π"},
-                {"func": "e^x", "domain": [0, 1], "solution": "(e-1)"},
-                {"func": "x", "domain": [1, 4], "solution": "5/2"},
-                {"func": "x^3", "domain": [0, 1], "solution": "1/4"}
+                {"func": "$x^2$", "domain": [0, 2], "solution": "$\\frac{4}{3}$"},
+                {"func": "$\\sin(x)$", "domain": [0, "π"], "solution": "$\\frac{2}{\\pi}$"},
+                {"func": "$e^x$", "domain": [0, 1], "solution": "$(e-1)$"},
+                {"func": "$x$", "domain": [1, 4], "solution": "$\\frac{5}{2}$"},
+                {"func": "$x^3$", "domain": [0, 1], "solution": "$\\frac{1}{4}$"}
             ],
             "hard": [
-                {"func": "x*sin(x)", "domain": [0, "π"], "solution": "π/2"},
-                {"func": "ln(x)", "domain": [1, "e"], "solution": "1-1/e"},
-                {"func": "x^2*e^x", "domain": [0, 1], "solution": "2e-2"},
-                {"func": "1/(1+x^2)", "domain": [0, 1], "solution": "π/4"},
-                {"func": "sqrt(x)", "domain": [0, 4], "solution": "4/3"}
+                {"func": "$x\\sin(x)$", "domain": [0, "π"], "solution": "$\\frac{\\pi}{2}$"},
+                {"func": "$\\ln(x)$", "domain": [1, "e"], "solution": "$1-\\frac{1}{e}$"},
+                {"func": "$x^2e^x$", "domain": [0, 1], "solution": "$2e-2$"},
+                {"func": "$\\frac{1}{1+x^2}$", "domain": [0, 1], "solution": "$\\frac{\\pi}{4}$"},
+                {"func": "$\\sqrt{x}$", "domain": [0, 4], "solution": "$\\frac{4}{3}$"}
             ]
         }
     },
     "Arc Length": {
-        "formula": "L = ∫[a,b] sqrt(1 + (f'(x))^2) dx",
+        "formula": "$L = \\int_{a}^{b} \\sqrt{1 + (f'(x))^2} dx$",
         "functions": {
             "easy": [
-                {"func": "x^2", "domain": [0, 1], "solution": "approx. 1.4789"},
-                {"func": "x^(3/2)", "domain": [0, 1], "solution": "approx. 1.1919"},
-                {"func": "2x+1", "domain": [0, 2], "solution": "sqrt(5)*2"},
-                {"func": "x^3", "domain": [0, 1], "solution": "approx. 1.0801"},
-                {"func": "sin(x)", "domain": [0, "π/2"], "solution": "approx. 1.9118"}
+                {"func": "$x^2$", "domain": [0, 1], "solution": "$\\approx 1.4789$"},
+                {"func": "$x^{3/2}$", "domain": [0, 1], "solution": "$\\approx 1.1919$"},
+                {"func": "$2x+1$", "domain": [0, 2], "solution": "$2\\sqrt{5}$"},
+                {"func": "$x^3$", "domain": [0, 1], "solution": "$\\approx 1.0801$"},
+                {"func": "$\\sin(x)$", "domain": [0, "π/2"], "solution": "$\\approx 1.9118$"}
             ],
             "hard": [
-                {"func": "ln(x)", "domain": [1, 3], "solution": "approx. 2.3861"},
-                {"func": "e^x", "domain": [0, 1], "solution": "approx. 1.1752"},
-                {"func": "cosh(x)", "domain": [0, 1], "solution": "sinh(1)"},
-                {"func": "x^2 - ln(x)", "domain": [1, 2], "solution": "approx. 3.1623"},
-                {"func": "parametric: x=cos(t), y=sin(t) for t∈[0,π]", "domain": [0, "π"], "solution": "π"}
+                {"func": "$\\ln(x)$", "domain": [1, 3], "solution": "$\\approx 2.3861$"},
+                {"func": "$e^x$", "domain": [0, 1], "solution": "$\\approx 1.1752$"},
+                {"func": "$\\cosh(x)$", "domain": [0, 1], "solution": "$\\sinh(1)$"},
+                {"func": "$x^2 - \\ln(x)$", "domain": [1, 2], "solution": "$\\approx 3.1623$"},
+                {"func": "$x = \\cos(t)$, $y = \\sin(t)$ for $t\\in[0,\\pi]$", "domain": [0, "π"], "solution": "$\\pi$"}
             ]
         }
     },
     "Surface Area": {
-        "formula": "S = 2π * ∫[a,b] f(x) * sqrt(1 + (f'(x))^2) dx",
+        "formula": "$S = 2\\pi \\int_{a}^{b} f(x) \\sqrt{1 + (f'(x))^2} dx$",
         "functions": {
             "easy": [
-                {"func": "x", "domain": [0, 3], "solution": "2π*4.5"},
-                {"func": "x^2", "domain": [0, 1], "solution": "approx. 2π*0.7169"},
-                {"func": "sqrt(x)", "domain": [0, 4], "solution": "approx. 2π*4.5177"},
-                {"func": "1", "domain": [0, 2], "solution": "2π*2"},
-                {"func": "x/2", "domain": [0, 4], "solution": "2π*4.1231"}
+                {"func": "$x$", "domain": [0, 3], "solution": "$2\\pi \\cdot 4.5$"},
+                {"func": "$x^2$", "domain": [0, 1], "solution": "$\\approx 2\\pi \\cdot 0.7169$"},
+                {"func": "$\\sqrt{x}$", "domain": [0, 4], "solution": "$\\approx 2\\pi \\cdot 4.5177$"},
+                {"func": "$1$", "domain": [0, 2], "solution": "$2\\pi \\cdot 2$"},
+                {"func": "$\\frac{x}{2}$", "domain": [0, 4], "solution": "$2\\pi \\cdot 4.1231$"}
             ],
             "hard": [
-                {"func": "x^3", "domain": [0, 1], "solution": "approx. 2π*0.6004"},
-                {"func": "e^x", "domain": [0, 1], "solution": "approx. 2π*1.1793"},
-                {"func": "sin(x)", "domain": [0, "π/2"], "solution": "approx. 2π*0.6366"},
-                {"func": "1/x", "domain": [1, 2], "solution": "approx. 2π*1.1478"},
-                {"func": "ln(x)", "domain": [1, 2], "solution": "approx. 2π*0.5593"}
+                {"func": "$x^3$", "domain": [0, 1], "solution": "$\\approx 2\\pi \\cdot 0.6004$"},
+                {"func": "$e^x$", "domain": [0, 1], "solution": "$\\approx 2\\pi \\cdot 1.1793$"},
+                {"func": "$\\sin(x)$", "domain": [0, "π/2"], "solution": "$\\approx 2\\pi \\cdot 0.6366$"},
+                {"func": "$\\frac{1}{x}$", "domain": [1, 2], "solution": "$\\approx 2\\pi \\cdot 1.1478$"},
+                {"func": "$\\ln(x)$", "domain": [1, 2], "solution": "$\\approx 2\\pi \\cdot 0.5593$"}
             ]
         }
     },
@@ -66,62 +144,138 @@ TOPICS = {
         "formula": "Various types",
         "functions": {
             "easy": [
-                {"func": "dy/dx = 2x", "domain": ["y(0)=1"], "solution": "y = x^2 + 1"},
-                {"func": "dy/dx = y", "domain": ["y(0)=1"], "solution": "y = e^x"},
-                {"func": "dy/dx = 3x^2", "domain": ["y(0)=2"], "solution": "y = x^3 + 2"},
-                {"func": "dy/dx = -y", "domain": ["y(0)=4"], "solution": "y = 4e^(-x)"},
-                {"func": "dy/dx = x+1", "domain": ["y(0)=-2"], "solution": "y = x^2/2 + x - 2"}
+                {"func": "$\\frac{dy}{dx} = 2x$", "domain": ["$y(0)=1$"], "solution": "$y = x^2 + 1$"},
+                {"func": "$\\frac{dy}{dx} = y$", "domain": ["$y(0)=1$"], "solution": "$y = e^x$"},
+                {"func": "$\\frac{dy}{dx} = 3x^2$", "domain": ["$y(0)=2$"], "solution": "$y = x^3 + 2$"},
+                {"func": "$\\frac{dy}{dx} = -y$", "domain": ["$y(0)=4$"], "solution": "$y = 4e^{-x}$"},
+                {"func": "$\\frac{dy}{dx} = x+1$", "domain": ["$y(0)=-2$"], "solution": "$y = \\frac{x^2}{2} + x - 2$"}
             ],
             "hard": [
-                {"func": "y'' + 4y = 0", "domain": ["y(0)=1, y'(0)=0"], "solution": "y = cos(2x)"},
-                {"func": "y'' - y = x", "domain": ["y(0)=0, y'(0)=1"], "solution": "y = e^x/2 - e^(-x)/2 - x"},
-                {"func": "y' + y = e^x", "domain": ["y(0)=0"], "solution": "y = xe^x"},
-                {"func": "y'' + 2y' + y = 0", "domain": ["y(0)=1, y'(0)=-1"], "solution": "y = (1-x)e^(-x)"},
-                {"func": "y'' - 2y' + y = x^2", "domain": ["y(0)=1, y'(0)=1"], "solution": "y = (x^2)/2 + 2x + 1"}
+                {"func": "$y'' + 4y = 0$", "domain": ["$y(0)=1$, $y'(0)=0$"], "solution": "$y = \\cos(2x)$"},
+                {"func": "$y'' - y = x$", "domain": ["$y(0)=0$, $y'(0)=1$"], "solution": "$y = \\frac{e^x}{2} - \\frac{e^{-x}}{2} - x$"},
+                {"func": "$y' + y = e^x$", "domain": ["$y(0)=0$"], "solution": "$y = xe^x$"},
+                {"func": "$y'' + 2y' + y = 0$", "domain": ["$y(0)=1$, $y'(0)=-1$"], "solution": "$y = (1-x)e^{-x}$"},
+                {"func": "$y'' - 2y' + y = x^2$", "domain": ["$y(0)=1$, $y'(0)=1$"], "solution": "$y = \\frac{x^2}{2} + 2x + 1$"}
             ]
         }
     },
     "Area and Volume": {
-        "formula": "A = ∫[a,b] f(x) dx, V = π * ∫[a,b] [f(x)]^2 dx",
+        "formula": "$A = \\int_{a}^{b} f(x) dx$, $V = \\pi \\int_{a}^{b} [f(x)]^2 dx$",
         "functions": {
             "easy": [
-                {"func": "f(x) = x^2, find area under the curve", "domain": [0, 3], "solution": "9"},
-                {"func": "f(x) = sin(x), find area under the curve", "domain": [0, "π"], "solution": "2"},
-                {"func": "f(x) = 4-x^2, find area under the curve", "domain": [-2, 2], "solution": "16/3"},
-                {"func": "f(x) = sqrt(x), find volume of revolution around x-axis", "domain": [0, 4], "solution": "16π/3"},
-                {"func": "f(x) = x, find volume of revolution around x-axis", "domain": [0, 2], "solution": "8π/3"}
+                {"func": "$f(x) = x^2$, find area under the curve", "domain": [0, 3], "solution": "$9$"},
+                {"func": "$f(x) = \\sin(x)$, find area under the curve", "domain": [0, "π"], "solution": "$2$"},
+                {"func": "$f(x) = 4-x^2$, find area under the curve", "domain": [-2, 2], "solution": "$\\frac{16}{3}$"},
+                {"func": "$f(x) = \\sqrt{x}$, find volume of revolution around x-axis", "domain": [0, 4], "solution": "$\\frac{16\\pi}{3}$"},
+                {"func": "$f(x) = x$, find volume of revolution around x-axis", "domain": [0, 2], "solution": "$\\frac{8\\pi}{3}$"}
             ],
             "hard": [
-                {"func": "Area between f(x) = x^2 and g(x) = x^3", "domain": [0, 1], "solution": "1/12"},
-                {"func": "Volume of solid bounded by z = 4-x^2-y^2 and z = 0", "domain": ["x^2+y^2≤4"], "solution": "8π"},
-                {"func": "Volume of solid formed by rotating region bounded by y = x^2, y = 0, x = 2 around y-axis", "domain": [0, 2], "solution": "8π/5"},
-                {"func": "Area between f(x) = sin(x) and g(x) = cos(x)", "domain": [0, "π/4"], "solution": "sqrt(2)-1"},
-                {"func": "Volume of solid formed by rotating region bounded by y = e^x, y = 0, x = 0, x = 1 around x-axis", "domain": [0, 1], "solution": "π(e^2-1)/2"}
+                {"func": "Area between $f(x) = x^2$ and $g(x) = x^3$", "domain": [0, 1], "solution": "$\\frac{1}{12}$"},
+                {"func": "Volume of solid bounded by $z = 4-x^2-y^2$ and $z = 0$", "domain": ["$x^2+y^2\\leq 4$"], "solution": "$8\\pi$"},
+                {"func": "Volume of solid formed by rotating region bounded by $y = x^2$, $y = 0$, $x = 2$ around y-axis", "domain": [0, 2], "solution": "$\\frac{8\\pi}{5}$"},
+                {"func": "Area between $f(x) = \\sin(x)$ and $g(x) = \\cos(x)$", "domain": [0, "π/4"], "solution": "$\\sqrt{2}-1$"},
+                {"func": "Volume of solid formed by rotating region bounded by $y = e^x$, $y = 0$, $x = 0$, $x = 1$ around x-axis", "domain": [0, 1], "solution": "$\\frac{\\pi(e^2-1)}{2}$"}
             ]
         }
     },
     "Parametric Curves and Equations": {
-        "formula": "x = x(t), y = y(t), Arc length = ∫[a,b] sqrt((dx/dt)^2 + (dy/dt)^2) dt",
+        "formula": "$x = x(t)$, $y = y(t)$, Arc length = $\\int_{a}^{b} \\sqrt{(\\frac{dx}{dt})^2 + (\\frac{dy}{dt})^2} dt$",
+        "functions": {
+            "easy": [
+                {"func": "$x = t$, $y = t^2$, find $\\frac{dy}{dx}$", "domain": ["$t$"], "solution": "$\\frac{dy}{dx} = 2t$"},
+                {"func": "$x = \\cos(t)$, $y = \\sin(t)$, find the arc length", "domain": [0, "π/2"], "solution": "$\\frac{\\pi}{2}$"},
+                {"func": "$x = t^2$, $y = t^3$, find $\\frac{dy}{dx}$", "domain": ["$t$"], "solution": "$\\frac{dy}{dx} = \\frac{3t}{2}$"},
+                {"func": "$x = 2t$, $y = t^2$, find the area under the curve", "domain": [0, 2], "solution": "$\\frac{4}{3}$"},
+                {"func": "$x = t$, $y = \\sin(t)$, find $\\frac{dy}{dx}$", "domain": ["$t$"], "solution": "$\\frac{dy}{dx} = \\cos(t)$"}
+            ],
+            "hard": [
+                {"func": "$x = e^t\\cos(t)$, $y = e^t\\sin(t)$, find $\\frac{dy}{dx}$", "domain": ["$t$"], "solution": "$\\frac{dy}{dx} = \\tan(t) + 1$"},
+                {"func": "$x = t-\\sin(t)$, $y = 1-\\cos(t)$, find the arc length", "domain": [0, "2π"], "solution": "$8$"},
+                {"func": "$x = \\ln(\\sec(t))$, $y = \\tan(t)$, find $\\frac{dy}{dx}$", "domain": ["$t$"], "solution": "$\\frac{dy}{dx} = \\sec^2(t)$"},
+                {"func": "$x = \\cos^3(t)$, $y = \\sin^3(t)$, find the area enclosed", "domain": [0, "2π"], "solution": "$\\frac{3\\pi}{8}$"},
+                {"func": "$x = \\cos(t)+t\\sin(t)$, $y = \\sin(t)-t\\cos(t)$, find the arc length", "domain": [0, "2π"], "solution": "$2\\pi\\sqrt{1+4\\pi^2}$"}
+            ]
+        }
+    },
+    "Infinite Sequences and Series": {
+        "formula": "$\\sum_{n=1}^{\\infty} a_n = a_1 + a_2 + a_3 + ...$",
+        "functions": {
+            "easy": [
+                {"func": "Determine if the sequence $a_n = \\frac{n+3}{2n+1}$ converges and find its limit", "domain": ["$n \\to \\infty$"], "solution": "Converges to $\\frac{1}{2}$"},
+                {"func": "Find the sum of the geometric series $\\sum_{n=0}^{\\infty} \\frac{1}{3^n}$", "domain": ["Geometric Series"], "solution": "$\\frac{3}{2}$"},
+                {"func": "Determine if the series $\\sum_{n=1}^{\\infty} \\frac{1}{n^2}$ converges", "domain": ["p-series"], "solution": "Converges (p-series with $p=2 > 1$)"},
+                {"func": "Find the first three non-zero terms in the Taylor series for $f(x) = e^x$ centered at $a = 0$", "domain": ["Taylor Series"], "solution": "$1 + x + \\frac{x^2}{2} + ...$"},
+                {"func": "Find the radius of convergence of the power series $\\sum_{n=1}^{\\infty} \\frac{x^n}{n}$", "domain": ["Power Series"], "solution": "$R = 1$"}
+            ],
+            "hard": [
+                {"func": "Test the convergence of the alternating series $\\sum_{n=1}^{\\infty} (-1)^{n+1}\\frac{\\ln(n)}{n}$", "domain": ["Alternating Series"], "solution": "Converges by the Alternating Series Test"},
+                {"func": "Find the radius and interval of convergence for $\\sum_{n=1}^{\\infty} \\frac{n^2 x^n}{3^n}$", "domain": ["Power Series"], "solution": "$R = 3$, interval of convergence is $(-3, 3)$"},
+                {"func": "Determine if the series $\\sum_{n=2}^{\\infty} \\frac{1}{n\\ln(n)}$ converges", "domain": ["Integral Test"], "solution": "Diverges by the Integral Test"},
+                {"func": "Find the sum of the series $\\sum_{n=1}^{\\infty} \\frac{1}{n(n+1)}$", "domain": ["Telescoping Series"], "solution": "$1$"},
+                {"func": "Find the Taylor series of $f(x) = \\ln(1+x)$ and its radius of convergence", "domain": ["Taylor Series"], "solution": "$\\sum_{n=1}^{\\infty} \\frac{(-1)^{n+1}x^n}{n}$, $R = 1$"}
+            ]
+        }
+    },
+    "Polar Coordinates": {
+        "formula": "$x = r\\cos(\\theta)$, $y = r\\sin(\\theta)$, Area = $\\frac{1}{2}\\int_{\\alpha}^{\\beta} r^2 d\\theta$",
         "functions": {
             "easy": [
-                {"func": "x = t, y = t^2, find dy/dx", "domain": ["t"], "solution": "dy/dx = 2t"},
-                {"func": "x = cos(t), y = sin(t), find the arc length", "domain": [0, "π/2"], "solution": "π/2"},
-                {"func": "x = t^2, y = t^3, find dy/dx", "domain": ["t"], "solution": "dy/dx = 3t/2"},
-                {"func": "x = 2t, y = t^2, find the area under the curve", "domain": [0, 2], "solution": "4/3"},
-                {"func": "x = t, y = sin(t), find dy/dx", "domain": ["t"], "solution": "dy/dx = cos(t)"}
+                {"func": "Convert the Cartesian point $(1, \\sqrt{3})$ to polar coordinates", "domain": ["Conversion"], "solution": "$r = 2$, $\\theta = \\frac{\\pi}{3}$"},
+                {"func": "Find the area enclosed by the circle $r = 3\\sin(\\theta)$", "domain": ["Polar Area"], "solution": "$\\frac{9\\pi}{2}$"},
+                {"func": "Convert the polar equation $r = 2$ to Cartesian form", "domain": ["Conversion"], "solution": "$x^2 + y^2 = 4$"},
+                {"func": "Find the area enclosed by $r = 2\\cos(\\theta)$", "domain": ["Polar Area"], "solution": "$2\\pi$"},
+                {"func": "Convert the Cartesian equation $x^2 + y^2 = 4y$ to polar form", "domain": ["Conversion"], "solution": "$r = 4\\sin(\\theta)$"}
             ],
             "hard": [
-                {"func": "x = e^t*cos(t), y = e^t*sin(t), find dy/dx", "domain": ["t"], "solution": "dy/dx = tan(t) + 1"},
-                {"func": "x = t-sin(t), y = 1-cos(t), find the arc length", "domain": [0, "2π"], "solution": "8"},
-                {"func": "x = ln(sec(t)), y = tan(t), find dy/dx", "domain": ["t"], "solution": "dy/dx = sec^2(t)"},
-                {"func": "x = cos^3(t), y = sin^3(t), find the area enclosed", "domain": [0, "2π"], "solution": "3π/8"},
-                {"func": "x = cos(t)+t*sin(t), y = sin(t)-t*cos(t), find the arc length", "domain": [0, "2π"], "solution": "2π*sqrt(1+4π^2)"}
+                {"func": "Find the area of the region enclosed by the lemniscate $r^2 = 4\\cos(2\\theta)$", "domain": ["Polar Area"], "solution": "$4$"},
+                {"func": "Find the area of the region inside $r = 1 + \\cos(\\theta)$ and outside $r = 1$", "domain": ["Polar Area"], "solution": "$\\frac{\\pi}{2}$"},
+                {"func": "Find the points of intersection of the polar curves $r = 1 + \\sin(\\theta)$ and $r = 1 - \\sin(\\theta)$", "domain": ["Polar Curves"], "solution": "$(0, 0)$ and $(1, \\frac{\\pi}{2})$, $(1, \\frac{3\\pi}{2})$"},
+                {"func": "Find the area of the region enclosed by the cardioid $r = 1 + \\cos(\\theta)$", "domain": ["Polar Area"], "solution": "$\\frac{3\\pi}{2}$"},
+                {"func": "Find the length of the spiral $r = \\theta$ for $0 \\leq \\theta \\leq 2\\pi$", "domain": ["Polar Arc Length"], "solution": "$\\frac{1}{2}\\sqrt{1+4\\pi^2} + \\frac{1}{2}\\ln(2\\pi + \\sqrt{1+4\\pi^2})$"}
+            ]
+        }
+    },
+    "Vector Calculus": {
+        "formula": "$\\vec{r}(t) = x(t)\\vec{i} + y(t)\\vec{j} + z(t)\\vec{k}$, $\\vec{v}(t) = \\vec{r}'(t)$, $\\vec{a}(t) = \\vec{v}'(t)$",
+        "functions": {
+            "easy": [
+                {"func": "Find the derivative of the vector function $\\vec{r}(t) = t^2\\vec{i} + \\sin(t)\\vec{j} + e^t\\vec{k}$", "domain": ["Vector Function"], "solution": "$\\vec{r}'(t) = 2t\\vec{i} + \\cos(t)\\vec{j} + e^t\\vec{k}$"},
+                {"func": "Find the unit tangent vector of $\\vec{r}(t) = \\cos(t)\\vec{i} + \\sin(t)\\vec{j}$ at $t = 0$", "domain": ["$t = 0$"], "solution": "$\\vec{T}(0) = \\vec{j}$"},
+                {"func": "Calculate $\\nabla f$ where $f(x,y,z) = x^2y + yz^2$", "domain": ["Gradient"], "solution": "$\\nabla f = 2xy\\vec{i} + (x^2 + z^2)\\vec{j} + 2yz\\vec{k}$"},
+                {"func": "Find the divergence of the vector field $\\vec{F}(x,y,z) = x^2\\vec{i} + 2xy\\vec{j} + yz\\vec{k}$", "domain": ["Divergence"], "solution": "$\\nabla \\cdot \\vec{F} = 2x + 2x + z = 4x + z$"},
+                {"func": "Find the curl of $\\vec{F}(x,y,z) = y\\vec{i} + z\\vec{j} + x\\vec{k}$", "domain": ["Curl"], "solution": "$\\nabla \\times \\vec{F} = (1-0)\\vec{i} + (1-0)\\vec{j} + (1-0)\\vec{k} = \\vec{i} + \\vec{j} + \\vec{k}$"}
+            ],
+            "hard": [
+                {"func": "Find the curvature of $\\vec{r}(t) = t\\vec{i} + t^2\\vec{j} + t^3\\vec{k}$ at $t = 1$", "domain": ["Curvature at $t = 1$"], "solution": "$\\kappa = \\frac{2\\sqrt{37}}{49\\sqrt{3}}$"},
+                {"func": "Verify Stokes' Theorem for $\\vec{F} = x^2\\vec{i} + xy\\vec{j} + z^2\\vec{k}$ on the hemisphere $z = \\sqrt{1-x^2-y^2}$, $z \\geq 0$", "domain": ["Stokes' Theorem"], "solution": "Both integrals equal $\\frac{\\pi}{2}$"},
+                {"func": "Use the Divergence Theorem to evaluate $\\iint_S \\vec{F} \\cdot \\vec{n} \\, dS$ where $\\vec{F}(x,y,z) = x\\vec{i} + y\\vec{j} + z\\vec{k}$ and $S$ is the sphere $x^2+y^2+z^2=4$", "domain": ["Divergence Theorem"], "solution": "$\\iint_S \\vec{F} \\cdot \\vec{n} \\, dS = \\iiint_V 3 \\, dV = 3 \\cdot \\frac{4}{3}\\pi \\cdot 4^{3/2} = 16\\pi$"},
+                {"func": "Find the potential function $f$ for the conservative vector field $\\vec{F} = (2x+y)\\vec{i} + (x+2z)\\vec{j} + (2y)\\vec{k}$", "domain": ["Potential Function"], "solution": "$f(x,y,z) = x^2 + xy + 2yz + C$"},
+                {"func": "Use Green's Theorem to evaluate $\\oint_C (y^2\\,dx + x^2\\,dy)$ where $C$ is the boundary of the region enclosed by $y = x^2$ and $y = 4$", "domain": ["Green's Theorem"], "solution": "$\\frac{256}{15}$"}
+            ]
+        }
+    },
+    "Partial Derivatives and Multiple Integrals": {
+        "formula": "$\\frac{\\partial f}{\\partial x}$, $\\frac{\\partial f}{\\partial y}$, $\\iint_D f(x,y) \\, dA$, $\\iiint_E f(x,y,z) \\, dV$",
+        "functions": {
+            "easy": [
+                {"func": "Find $\\frac{\\partial z}{\\partial x}$ and $\\frac{\\partial z}{\\partial y}$ for $z = x^2 + 3xy - y^3$", "domain": ["Partial Derivatives"], "solution": "$\\frac{\\partial z}{\\partial x} = 2x + 3y$, $\\frac{\\partial z}{\\partial y} = 3x - 3y^2$"},
+                {"func": "Evaluate $\\iint_D (x + y) \\, dA$ where $D = \\{(x, y) | 0 \\leq x \\leq 1, 0 \\leq y \\leq 2\\}$", "domain": ["Double Integral"], "solution": "$3$"},
+                {"func": "Find all critical points of $f(x,y) = x^2 + y^2 - 4x - 6y + 12$", "domain": ["Critical Points"], "solution": "$(2, 3)$"},
+                {"func": "Convert the double integral $\\iint_D x^2y \\, dA$ to polar coordinates where $D$ is the disc $x^2 + y^2 \\leq 4$", "domain": ["Change to Polar"], "solution": "$\\int_0^{2\\pi} \\int_0^2 r^3 \\cos^2(\\theta)\\sin(\\theta) \\, dr \\, d\\theta$"},
+                {"func": "Evaluate $\\iint_D xy \\, dA$ where $D$ is the triangle with vertices $(0,0)$, $(1,0)$, and $(0,1)$", "domain": ["Double Integral"], "solution": "$\\frac{1}{24}$"}
+            ],
+            "hard": [
+                {"func": "Find the absolute maximum and minimum values of $f(x,y) = 2x^2 + y^2 - 4x + 6y + 10$ on the closed disc $x^2 + y^2 \\leq 25$", "domain": ["Extrema on Region"], "solution": "Maximum: $135$ at $(5,0)$, Minimum: $1$ at $(1,-3)$"},
+                {"func": "Evaluate $\\iiint_E xy^2z^3 \\, dV$ where $E$ is the solid bounded by $x=0$, $y=0$, $z=0$, $x+y+z=1$", "domain": ["Triple Integral"], "solution": "$\\frac{1}{840}$"},
+                {"func": "Use Lagrange multipliers to find the maximum value of $f(x,y) = xy$ subject to the constraint $x^2 + y^2 = 8$", "domain": ["Lagrange Multipliers"], "solution": "$4$ at $(\\pm 2, \\pm 2)$"},
+                {"func": "Change the order of integration in $\\int_0^1 \\int_y^1 e^{xy} \\, dx \\, dy$", "domain": ["Change of Order"], "solution": "$\\int_0^1 \\int_0^x e^{xy} \\, dy \\, dx$"},
+                {"func": "Evaluate $\\iint_D \\frac{1}{1+x^2+y^2} \\, dA$ where $D = \\{(x,y) | x^2 + y^2 \\leq 4\\}$", "domain": ["Double Integral"], "solution": "$\\pi\\ln(5)$"}
             ]
         }
     }
 }
 
-# Function to generate a single question
+# Function to generate a question for a given topic and difficulty
 def generate_question(topic_name, difficulty):
     topic_data = TOPICS[topic_name]
     formula = topic_data["formula"]
@@ -142,7 +296,7 @@ def generate_question(topic_name, difficulty):
     if difficulty == "easy":
         question = f"Find the {topic_name.lower()} of {func} over the domain {domain_str}."
         solution_text = f"Step 1: Apply the formula for {topic_name.lower()}: {formula}\n\n"
-        solution_text += f"Step 2: Substitute f(x) = {func} and evaluate over {domain_str}\n\n"
+        solution_text += f"Step 2: Substitute $f(x) = {func}$ and evaluate over {domain_str}\n\n"
         solution_text += f"Step 3: Solve the resulting integral or calculation\n\n"
         solution_text += f"Final Answer: {solution}"
     else:
@@ -150,69 +304,99 @@ def generate_question(topic_name, difficulty):
         solution_text = f"Step 1: Apply the formula for {topic_name.lower()}: {formula}\n\n"
         solution_text += f"Step 2: For {func}, substitute into the formula and evaluate over {domain_str}\n\n"
         solution_text += f"Step 3: This requires advanced integration techniques or careful analysis\n\n"
-        solution_text += f"Step 4: After simplification and evaluation of the integral\n\n"
         solution_text += f"Final Answer: {solution}"
     
-    return question, solution_text
+    return {
+        "topic": topic_name,
+        "difficulty": difficulty,
+        "question": question,
+        "solution": solution_text
+    }
+
+# Store the latest generated questions
+latest_questions = []
 
-# Function to generate multiple questions
-def generate_multiple_questions(topic_name, difficulty, count):
-    questions = []
-    solutions = []
+# Generate questions function for Gradio
+def generate_calculus_questions(topic, difficulty, count):
+    global latest_questions
+    latest_questions = []
     
-    for _ in range(count):
-        question, solution = generate_question(topic_name, difficulty)
-        questions.append(question)
-        solutions.append(solution)
+    for _ in range(int(count)):
+        question_data = generate_question(topic, difficulty)
+        latest_questions.append(question_data)
     
-    combined_questions = "\n\n".join([f"{i+1}. {q}" for i, q in enumerate(questions)])
-    combined_solutions = "\n\n" + "-"*50 + "\n\n".join([f"Solution {i+1}:\n{s}" for i, s in enumerate(solutions)])
+    # Format the output for display
+    result = ""
+    for i, q in enumerate(latest_questions):
+        result += f"Question {i+1}: {q['question']}\n\n"
+        result += f"Solution {i+1}: {q['solution']}\n\n"
+        result += "-" * 40 + "\n\n"
     
-    return combined_questions, combined_solutions
+    return result
 
-# Gradio app function
-def generate_calculus_questions(topic, difficulty, count):
-    count = int(count)  # Convert to int in case it's a string
-    questions, solutions = generate_multiple_questions(topic, difficulty, count)
-    return questions, solutions
+# Function to export questions to JSON
+def export_to_json():
+    if not latest_questions:
+        return None
+    
+    # Create a JSON file
+    timestamp = datetime.now().strftime("%Y%m%d_%H%M%S")
+    json_data = {
+        "generated_at": timestamp,
+        "questions": latest_questions
+    }
+    
+    # Create a temporary file
+    with tempfile.NamedTemporaryFile(mode="w+", delete=False, suffix=".json") as temp_file:
+        json.dump(json_data, temp_file, indent=2)
+        temp_file_path = temp_file.name
+    
+    return temp_file_path
 
 # Create the Gradio interface
-with gr.Blocks(title="Calculus Question Generator") as demo:
-    gr.Markdown("# Calculus Question Generator")
-    gr.Markdown("Select a topic, difficulty level, and the number of questions to generate.")
+with gr.Blocks(title="Math Mento - Calculus Questions Generator") as demo:
+    gr.Markdown("# Math Mento - Calculus Questions Generator")
+    gr.Markdown("Generate LaTeX-formatted calculus practice questions with solutions based on James Stewart's calculus textbook")
     
     with gr.Row():
         with gr.Column():
             topic = gr.Dropdown(
                 choices=list(TOPICS.keys()),
                 label="Calculus Topic",
-                value="Average Value"
+                value="Limits and Continuity"
             )
             difficulty = gr.Radio(
                 choices=["easy", "hard"],
-                label="Difficulty Level",
+                label="Difficulty",
                 value="easy"
             )
             count = gr.Slider(
                 minimum=1,
                 maximum=10,
-                value=3,
                 step=1,
+                value=3,
                 label="Number of Questions"
             )
             generate_button = gr.Button("Generate Questions")
+            export_button = gr.Button("Export to JSON")
         
         with gr.Column():
-            questions_output = gr.Textbox(label="Generated Questions", lines=10)
-            solutions_output = gr.Textbox(label="Solutions", lines=15)
+            output = gr.Markdown()
+            json_file = gr.File(label="Exported JSON")
     
     generate_button.click(
         generate_calculus_questions,
         inputs=[topic, difficulty, count],
-        outputs=[questions_output, solutions_output]
+        outputs=output
+    )
+    
+    export_button.click(
+        export_to_json,
+        inputs=[],
+        outputs=json_file
     )
     
-    gr.Markdown("### Created by KamogeloMosiai")
+    gr.Markdown("### Created by Kamogelo Mosia | Math Mento © 2025")
 
 # Launch the app
 if __name__ == "__main__":