Update app.py

app.py

@@ -514,6 +514,7 @@ def generate_question(subject, difficulty, question_type):
 
         system_prompt = f"""You are an expert mathematics professor creating a {difficulty_params['description']} exam question.
 STRICT REQUIREMENTS:
+0. Start out with a heading in bold: Question
 1. Write exactly 1 {question_type} question on {subject} covering {selected_topic}.
 2. Difficulty Level Guidelines:
    {difficulty_params['description'].upper()}
@@ -530,7 +531,7 @@ STRICT REQUIREMENTS:
    - Put each solution step on its own line in $$ $$
    - DO NOT use \\begin{{aligned}} or similar environments
 5. Include a detailed solution
-   - Begin the solution with a heading in bold and larger font size: Original Solution
+   - Begin the solution with a heading in bold: Original Solution
    - If the question involves geometry make sure to identify any general geometric formulas that apply, For example:
         * Areas/volumes of common shapes and solids
         * Cross-sectional areas of geometric figures
@@ -540,7 +541,7 @@ STRICT REQUIREMENTS:
         * ensure integration bounds align with the physical direction of the process being modeled
 6. Maintain clear formatting
 7. At the end of the solution output, print SymPy code that you would use to solve or verify the main equations in the question 
-   and give this section a heading in bold and larger font size: SymPy Verification
+   and give this section a heading in bold: SymPy Verification
 8. Observe the folloiwng SymPy Guidelines
 {SYMPY_GUIDELINES}"""
 
@@ -669,7 +670,7 @@ def check_and_resolve_discrepancy(initial_response, sympy_output):
         The first, called Original solution, is a complete solution.
         The second, called SymPy Verification, will only provide the final answer.
 
-        Begin this section with a heading in bold and larger font size: Comparison of SymPy Verifiation with Original Solution
+        Begin this section with a heading in bold: Comparison of SymPy Verifiation with Original Solution
         
         If the SymPy Verification answer is consistent with the final answer Original solution,
         then please say that they are consistent and briefly explain why. 
@@ -779,6 +780,8 @@ Revised Solution to Verify:
 
 Please follow these steps exactly:
 
+0. Begin with a heading in bold: Expert Analysis of Revised Solution
+
 1. First, analyze the solution for:
    - Mathematical correctness
    - Missing cases or assumptions
@@ -786,7 +789,8 @@ Please follow these steps exactly:
    - Necessary conditions and edge cases
    - Any subtle errors or oversights
 
-2. After your analysis, write exactly this phrase:
+2. After your analysis, include a heading in bold: Final Verified Solution
+   Then write exactly this phrase:
    "Here is the complete verified solution:"
 
 3. Then write out the ENTIRE solution from beginning to end, including:
@@ -804,7 +808,6 @@ Your complete solution must:
 - Maintain proper LaTeX formatting with $ for inline math and $ on separate lines
 - Include any relevant SymPy code for verification
 
-Begin this section with a heading in bold and larger font size: Final Verified Solution
 Remember to write out the complete solution even if you only need to add a few steps - the goal is to have a single, complete, verified solution that includes everything necessary for full mathematical rigor."""
 
     try: