Create app.py

app.py

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+import gradio as gr
+import json
+import random
+import math
+
+# Define a list of topics with specific formulas and question templates
+TOPICS = {
+    "Average Value": {
+        "formula": "f_avg = (1/(b-a)) * ∫[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"}
+            ],
+            "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"}
+            ]
+        }
+    },
+    "Arc Length": {
+        "formula": "L = ∫[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"}
+            ],
+            "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"}
+            ]
+        }
+    },
+    "Surface Area": {
+        "formula": "S = 2π * ∫[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"}
+            ],
+            "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"}
+            ]
+        }
+    },
+    "Differential Equations": {
+        "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"}
+            ],
+            "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"}
+            ]
+        }
+    },
+    "Area and Volume": {
+        "formula": "A = ∫[a,b] f(x) dx, V = π * ∫[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"}
+            ],
+            "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"}
+            ]
+        }
+    },
+    "Parametric Curves and Equations": {
+        "formula": "x = x(t), y = y(t), Arc length = ∫[a,b] sqrt((dx/dt)^2 + (dy/dt)^2) dt",
+        "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)"}
+            ],
+            "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)"}
+            ]
+        }
+    }
+}
+
+# Function to generate a single question
+def generate_question(topic_name, difficulty):
+    topic_data = TOPICS[topic_name]
+    formula = topic_data["formula"]
+    
+    # Select a random function from the available ones for this topic and difficulty
+    function_data = random.choice(topic_data["functions"][difficulty])
+    func = function_data["func"]
+    domain = function_data["domain"]
+    solution = function_data["solution"]
+    
+    # Format domain for display
+    if isinstance(domain, list) and len(domain) == 2:
+        domain_str = f"[{domain[0]}, {domain[1]}]"
+    else:
+        domain_str = str(domain)
+    
+    # Create question and solution based on 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 3: Solve the resulting integral or calculation\n\n"
+        solution_text += f"Final Answer: {solution}"
+    else:
+        question = f"Compute the {topic_name.lower()} for {func} over {domain_str}."
+        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
+
+# Function to generate multiple questions
+def generate_multiple_questions(topic_name, difficulty, count):
+    questions = []
+    solutions = []
+    
+    for _ in range(count):
+        question, solution = generate_question(topic_name, difficulty)
+        questions.append(question)
+        solutions.append(solution)
+    
+    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)])
+    
+    return combined_questions, combined_solutions
+
+# 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
+
+# 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.Row():
+        with gr.Column():
+            topic = gr.Dropdown(
+                choices=list(TOPICS.keys()),
+                label="Calculus Topic",
+                value="Average Value"
+            )
+            difficulty = gr.Radio(
+                choices=["easy", "hard"],
+                label="Difficulty Level",
+                value="easy"
+            )
+            count = gr.Slider(
+                minimum=1,
+                maximum=10,
+                value=3,
+                step=1,
+                label="Number of Questions"
+            )
+            generate_button = gr.Button("Generate Questions")
+        
+        with gr.Column():
+            questions_output = gr.Textbox(label="Generated Questions", lines=10)
+            solutions_output = gr.Textbox(label="Solutions", lines=15)
+    
+    generate_button.click(
+        generate_calculus_questions,
+        inputs=[topic, difficulty, count],
+        outputs=[questions_output, solutions_output]
+    )
+    
+    gr.Markdown("### Created by KamogeloMosiai")
+
+# Launch the app
+if __name__ == "__main__":
+    demo.launch()