Update app.py

app.py

@@ -477,7 +477,7 @@ ADDITIONAL PROOF GUIDELINES:
 def get_difficulty_parameters(difficulty_level):
     """Return specific parameters and constraints based on difficulty level"""
     parameters = {
-        1: {  # Very Easy
+        1: {    Very Easy
             "description": "suitable for beginners",
             "constraints": [
                 "Use only basic concepts and straightforward calculations",
@@ -836,17 +836,17 @@ def generate_question(subject, difficulty, question_type, subtopic=None, use_enh
         difficulty_params = get_difficulty_parameters(difficulty)
         problem_type_addition = get_problem_type_addition(question_type)
 
-        system_prompt = f"""You are a mathematics professor. Write exactly one {question_type} exam question on {subject} covering {selected_topic} that can be solved analytically, without numerical methods.
-STRICT REQUIREMENTS:
-1. Begin the output with the text "Here is a test question that is a {question_type} 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'])}
-   {problem_type_addition}
-3. Style Reference:
-   Question should be {difficulty_params['example_style']}
-4. For LaTeX formatting:
+        system_prompt = f"""You are a mathematics professor. 
+        
+Part I. Write 10 {question_type} exam questions that can be solved analytically, without numerical methods,
+        in increasing order of difficulty from easiest to hardest that would test a student's ability on the topic {selected_topic} in {subject}. 
+        The easiest question should be the most basic problem on {selected_topic}. The hardest two questions would be very tricky even for an undergraduate 
+        mathematics major at a top university.
+
+Part II. Now select the problem that is number {difficulty} on your exam, state the question again and provide a solution.
+        
+1. Begin the output for Part II with the text "Here is a test question that is a {question_type} question on {subject} covering {selected_topic} of difficulty level {difficulty} out of 10." 
+2. Important LaTeX formatting for both Part I and Part II
    - Make sure that the question statement uses proper LaTeX math mode 
    - Use $ for inline math
    - Use $$ on separate lines for equations and solutions
@@ -854,7 +854,7 @@ STRICT REQUIREMENTS:
    - DO NOT use \\begin{{aligned}} or similar environments
    - When writing questions involving currency expressed in dollars NEVER use the `$` symbol as it will be interepreted as math mode. ALWAYS write out the word dollars.
       * Example: 1000 dollars
-5. Include a detailed solution
+3. For the detailed soltuion
    - Begin the solution with "Here is a detailed solution to the test question."
    - If the question involves geometry make sure to identify any general geometric formulas that apply, For example:
         * Areas/volumes of common shapes and solids
@@ -867,11 +867,11 @@ STRICT REQUIREMENTS:
         * NO part of the solution may resort to or be based on numerical analysis.
         * The only numerical calculations that should be done are those that could be done on a simple scientific calculator.
         * Make sure to simplify completely as far as analytical methods will allow
-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
+4. Maintain clear formatting
+5. At the end of the solution output, print SymPy code that you would use to solve or verify the main equations in the question 
+6. Observe the folloiwng SymPy Guidelines
 {SYMPY_GUIDELINES}
-9. For problems where the subject is Real Analysis, observe the following guidelines:
+7. For problems where the subject is Real Analysis, observe the following guidelines:
 
 a. **Justify Every Step**  
    - Provide detailed reasoning for each step and explicitly justify every bounding argument, inequality, or limit claim.  
@@ -917,28 +917,28 @@ j. **Concluding and Intuitive Explanations**
    - Conclude with an intuitive explanation of why the result makes sense, possibly connecting it to known theorems or simple examples.  
    - In notes after the proof, highlight potential sources of confusion for students and clarify tricky aspects of the problem.  
 
-10. If you specify a quadrant restriction (e.g. "in the first quadrant") in a problem with calculating area between lines/curves or volume between surfaces,
+8. If you specify a quadrant restriction (e.g. "in the first quadrant") in a problem with calculating area between lines/curves or volume between surfaces,
 make sure the question is CLEAR about what regions you intend to be included in the solution, by breaking up the question. Examples:
 - NOT CLEAR question: Find the area of the region bounded by the curves y = sin(x), y = cos(x), and x = 7*pi/4 in the first quadrant.
 - CLEAR question: Find the area of the region bounded by the curves y = sin(x), y = cos(x), and x = 7*pi/4. Then find the area of that region that intersects with the first quadrant.
 
-11. When finding critical points in multivariable calculus:
+9. When finding critical points in multivariable calculus:
    - Always check what happens when any variable equals zero (except where undefined)
    - Just because a point is ruled out of the domain doesn't mean that entire line/curve is ruled out 
    - When the Hessian is inconclusive, evaluate the function along the critical curves to determine behavior
    - Don't rely solely on the Hessian - consider direct function evaluation and nearby points
 
-12. When using symmetry arguments:
+10. When using symmetry arguments:
    - Explicitly state what is symmetric
    - Identify the axis/plane of symmetry
 
-13. In calculus do not forget opportunities to apply power-reduction formulas for trig functions
+11. In calculus do not forget opportunities to apply power-reduction formulas for trig functions
    - e.g.: Integral from 0 to pi of [cos(theta)]^(2n) d(theta) = (pi / 2^(2n)) * (2n choose n), where choose is the combinatorial choose function
 
-14. In expanding or factoring polynomial expressions, be careful not to make errors
+12. In expanding or factoring polynomial expressions, be careful not to make errors
    - (1+u^2)^2 is equal to (1+2u^2+u^4), NOT equal to (1+3u^2+u^4) 
 
-15. When finding points where dy/dx = 0 in parametric equations:
+13. When finding points where dy/dx = 0 in parametric equations:
  - (a) First find the ratio dy/dx = (dy/dt)/(dx/dt)
  - (b) Find t-values where this ratio equals 0
  - (c) CRITICAL: For any t-values where both dy/dt = 0 AND dx/dt = 0:
@@ -953,7 +953,7 @@ make sure the question is CLEAR about what regions you intend to be included in
    - Verify the point lies on the curve
    - State whether it's a regular point or special point (cusp, corner, etc.)
 
-16. Be careful with trigonometric expressions involving powers
+14. Be careful with trigonometric expressions involving powers
    - Example: solving sin^2(x)=cos(x) can be solved as 1-cos^2(x)=cos(x)
 
 """