Update app.py

app.py

@@ -514,7 +514,8 @@ 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:
-1. Write exactly 1 {question_type} question on {subject} covering {selected_topic} that can be solved analytically (without numerical methods)
+1. Write exactly 1 {question_type} question on {subject} covering {selected_topic} that can be solved analytically without numerical methods. 
+   A question where any part of the solution must resort to numerical methdos is invalid.
 2. Difficulty Level Guidelines:
    {difficulty_params['description'].upper()}
    Follow these specific constraints:
@@ -538,7 +539,7 @@ STRICT REQUIREMENTS:
    - When setting up differential equations either in calculus or differential equation applications
         * carefully consider the direction of change in variables
         * ensure integration bounds align with the physical direction of the process being modeled
-   - The solution must be analytical. It must not rely on numerical methods. 
+   - The solution must be analytical. It must not rely on numerical methods. NO part of the solution may resort to or be based on numerical analysis.
 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 
 8. Observe the folloiwng SymPy Guidelines