Update app.py

app.py

@@ -778,6 +778,10 @@ Part I. Write 10 {question_type} exam questions that can be solved analytically,
         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.
+        Observe the following about {question_type} questions: {problem_type_addition}.
+        Note: 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.
 
 Part II. Now select the problem that is number {difficulty} on your exam, state the question again and provide a solution.
         
@@ -853,11 +857,6 @@ 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.  
 
-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.
-
 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