Update app.py

app.py

@@ -30,15 +30,48 @@ request_history = deque(maxlen=1000)
 SYMPY_GUIDELINES = """
 When writing SymPy code to verify solutions:
 
-1. Variable Declaration and Functions:
-   - Always define symbolic variables first, for example:
+1. Variable Declaration and Expressions:
+   - ALWAYS create symbolic expressions instead of literal numbers when working with mathematical operations:
      ```python
-     x, y, z = symbols('x y z')  # For multiple variables
-     t = Symbol('t')            # For single variables
+     # CORRECT:
+     x = Symbol('x')
+     expr = x + 1  # Creates a symbolic expression
+     
+     # INCORRECT:
+     expr = 1  # This is just a number, can't be differentiated
      ```
-   - Use Abs() for absolute value (not abs())
-   - Define functions using Function() class when needed
-
+   - For polynomials and functions:
+     ```python
+     # CORRECT:
+     x = Symbol('x')
+     p = x**2 + 2*x + 1  # Creates a polynomial expression
+     
+     # INCORRECT:
+     p = 1  # This won't work for operations like diff()
+     ```
+   - When verifying operator actions:
+     ```python
+     # CORRECT:
+     x = Symbol('x')
+     def verify_operator(p):
+         x = Symbol('x')  # Always use Symbol inside functions too
+         return p.subs(x, 1)  # Substitute values after creating expression
+     
+     # INCORRECT:
+     def verify_operator(p):
+         return p  # Passing raw numbers won't work
+     ```
+   - For integration bounds:
+     ```python
+     # CORRECT:
+     t = Symbol('t')
+     expr = t**2
+     result = integrate(expr, (t, 0, 1))
+     
+     # INCORRECT:
+     result = integrate(2, (t, 0, 1))  # Can't integrate a number
+     ```
+     
 2. Solving and Computing:
    - Never use strings in solve() or other SymPy functions:
      CORRECT:   solve(eq, x)