Update app.py

app.py

@@ -154,23 +154,46 @@ def generate_question(subject, difficulty, question_type):
         logger.debug(f"Selected topic: {selected_topic}")
         
         difficulty_params = get_difficulty_parameters(difficulty)
-        
-        # Enhanced prompt for difficulty level 5
-        if difficulty == 5:
-            system_prompt = f"""You are an expert mathematics professor creating a graduate-level exam question.
+        [Previous code remains the same until the system_prompt section...]
+
+        if question_type == "application":
+            application_addition = """
+The application question MUST:
+- Present a real-world scenario or practical problem
+- Require modeling the situation mathematically
+- Connect abstract mathematical concepts to concrete situations
+- Include realistic context and data
+- Require students to:
+    1. Identify relevant mathematical concepts
+    2. Translate the practical problem into mathematical terms
+    3. Solve using appropriate mathematical techniques
+    4. Interpret the results in the context of the original problem
+
+Example contexts might include:
+- Physics applications (motion, forces, work)
+- Engineering scenarios (optimization, rates of change)
+- Economics problems (cost optimization, growth models)
+- Biological systems (population growth, reaction rates)
+- Business applications (profit maximization, inventory management)
+- Social science applications (demographic models, social network analysis)
+- Data science applications (regression, statistical analysis)
+"""
+            if difficulty == 5:
+                system_prompt = f"""You are an expert mathematics professor creating a graduate-level exam question.
 STRICT REQUIREMENTS:
-1. Write exactly 1 graduate-level {question_type} question on {subject} covering {selected_topic}.
+1. Write exactly 1 graduate-level application question on {subject} covering {selected_topic}.
 2. Advanced Difficulty Requirements:
    This question must be suitable for PhD qualifying exams or advanced competitions.
    MUST include:
-   - Novel applications of theoretical concepts
-   - Graduate-level mathematical reasoning
-   - Unexpected connections between different areas of {subject}
+   - Novel applications of theoretical concepts to complex real-world scenarios
+   - Graduate-level mathematical reasoning in practical contexts
+   - Sophisticated modeling of real situations
    - Creative problem-solving approaches
-   - Rigorous proof requirements where applicable
+   - Multiple stages of mathematical modeling and analysis
    
    Follow these specific constraints:
    {chr(10).join(f'   - {c}' for c in difficulty_params['constraints'])}
+   {application_addition}
 3. Style Reference:
    Question should be {difficulty_params['example_style']}
 4. The question MUST:
@@ -183,16 +206,20 @@ STRICT REQUIREMENTS:
    - Use $$ on separate lines for equations and solutions
    - Put each solution step on its own line in $$ $$
    - DO NOT use \\begin{{aligned}} or similar environments
-6. Include a detailed solution with thorough explanations of advanced concepts used
+6. Include a detailed solution with thorough explanations of:
+   - How to model the situation
+   - Why specific mathematical techniques were chosen
+   - How to interpret the results
 7. Maintain clear, precise formatting"""
-        else:
-            system_prompt = f"""You are an expert mathematics professor creating a {difficulty_params['description']} exam question.
+            else:
+                system_prompt = f"""You are an expert mathematics professor creating a {difficulty_params['description']} exam question.
 STRICT REQUIREMENTS:
-1. Write exactly 1 {question_type} question on {subject} covering {selected_topic}.
+1. Write exactly 1 application question on {subject} covering {selected_topic}.
 2. Difficulty Level Guidelines:
    {difficulty_params['description'].upper()}
    Follow these specific constraints:
    {chr(10).join(f'   - {c}' for c in difficulty_params['constraints'])}
+   {application_addition}
 3. Style Reference:
    Question should be {difficulty_params['example_style']}
 4. For LaTeX formatting:
@@ -200,8 +227,12 @@ STRICT REQUIREMENTS:
    - Use $$ on separate lines for equations and solutions
    - Put each solution step on its own line in $$ $$
    - DO NOT use \\begin{{aligned}} or similar environments
-5. Include a detailed solution
+5. Include a detailed solution that explains:
+   - How to model the situation
+   - Why specific mathematical techniques were chosen
+   - How to interpret the results
 6. Maintain clear formatting"""
+        else:
         
         logger.debug("Sending request to Anthropic API")
         message = anthropic.messages.create(