'''simple docstring'''

from __future__ import annotations

from collections.abc import Callable



def  _lowerCAmelCase				(				__a			,      __a			,      __a			,      __a = 1_00			,      )  ->      float:
     '''simple docstring'''







     _UpperCamelCase  :str       =x_start
     _UpperCamelCase  :int       =fnc(__a      )
     _UpperCamelCase  :Any       =0.0

     for _ in range(__a      ):
          # Approximates small segments of curve as linear and solve
          # for trapezoidal area
          _UpperCamelCase  :List[Any]       =(x_end - x_start) / steps + xa
          _UpperCamelCase  :Any       =fnc(__a      )
          area += abs(fxa + fxa      ) * (xa - xa) / 2

          # Increment step
          _UpperCamelCase  :Union[str, Any]       =xa
          _UpperCamelCase  :str       =fxa
     return area


if __name__ == "__main__":



      def  _lowerCAmelCase				(				__a      )  ->      Optional[Any]:
           '''simple docstring'''







           return x**3

      print("""f(x) = x^3""")
      print("""The area between the curve, x = -10, x = 10 and the x axis is:""")
      _lowerCamelCase :				Union[str, Any]														= 10
      while i <= 10_00_00:
            _lowerCamelCase :				List[Any]														= trapezoidal_area(f, -5, 5, i)
            print(f"with {i} steps: {area}")
            i *= 10
'''simple docstring'''

from .balanced_parentheses import balanced_parentheses
from .stack import Stack



def  _lowerCAmelCase				(				__a      )  ->      int:
     '''simple docstring'''







     return {"+": 1, "-": 1, "*": 2, "/": 2, "^": 3}.get(__a			,      -1      )



def  _lowerCAmelCase				(				__a      )  ->      str:
     '''simple docstring'''







     if not balanced_parentheses(__a      ):
          raise ValueError("""Mismatched parentheses"""      )
     _UpperCamelCase  :Stack[str]       =Stack()
     _UpperCamelCase  :Optional[int]       =[]
     for char in expression_str:
          if char.isalpha() or char.isdigit():
               postfix.append(__a      )
          elif char == "(":
               stack.push(__a      )
          elif char == ")":
               while not stack.is_empty() and stack.peek() != "(":
                    postfix.append(stack.pop()      )
               stack.pop()
          else:
               while not stack.is_empty() and precedence(__a      ) <= precedence(stack.peek()      ):
                    postfix.append(stack.pop()      )
               stack.push(__a      )
     while not stack.is_empty():
          postfix.append(stack.pop()      )
     return " ".join(__a      )


if __name__ == "__main__":
      from doctest import testmod

      testmod()
      _lowerCamelCase :				Tuple														= """a+b*(c^d-e)^(f+g*h)-i"""

      print("""Infix to Postfix Notation demonstration:\n""")
      print("""Infix notation: """ + expression)
      print("""Postfix notation: """ + infix_to_postfix(expression))