Update app.py

app.py

@@ -371,12 +371,14 @@ STRICT REQUIREMENTS:
 7. Maintain clear, precise formatting
 8. At the end of the LaTeX solution output, print SymPy code that you would use to solve or verify the main equations in the question.
 9. When writing SymPy code to verify solutions:
-   - Import specific functions like this: from sympy import Symbol, solve, limit, Abs, integrate
-   - Use ONLY SymPy functions - do not use NumPy, SciPy, or other libraries
-   - For numerical integration, use SymPy's integrate() instead of scipy.integrate.quad()
-   - For any numerical computations, use SymPy's native functions
+   - Start with essential imports: from sympy import * 
+   - Or use specific imports as needed: from sympy import Symbol, solve, limit, Abs, integrate, Function, diff, sin, cos
+   - DO NOT use NumPy, SciPy, or other libraries
+   - For numerical integration, use integrate() instead of scipy.integrate.quad()
+   - For any numerical computations, use native SymPy functions
    - Always define symbolic variables using Symbol() before using them
    - Use Abs() for absolute value (not abs())
+   - Define functions using Function() class when needed
    - Include print statements for ALL calculations and results
    - Print intermediate steps and final answers
    - Print variable values after they are computed
@@ -412,12 +414,14 @@ STRICT REQUIREMENTS:
    - Print variable values after they are computed
    - Format numerical results using evalf() for decimal
 9. When writing SymPy code to verify solutions:
-   - Import specific functions like this: from sympy import Symbol, solve, limit, Abs, integrate
-   - Use ONLY SymPy functions - do not use NumPy, SciPy, or other libraries
-   - For numerical integration, use SymPy's integrate() instead of scipy.integrate.quad()
-   - For any numerical computations, use SymPy's native functions
+   - Start with essential imports: from sympy import * 
+   - Or use specific imports as needed: from sympy import Symbol, solve, limit, Abs, integrate, Function, diff, sin, cos
+   - DO NOT use NumPy, SciPy, or other libraries
+   - For numerical integration, use integrate() instead of scipy.integrate.quad()
+   - For any numerical computations, use native SymPy functions
    - Always define symbolic variables using Symbol() before using them
    - Use Abs() for absolute value (not abs())
+   - Define functions using Function() class when needed
    - Include print statements for ALL calculations and results
    - Print intermediate steps and final answers
    - Print variable values after they are computed