'''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))


'''simple docstring'''

from __future__ import annotations

from collections.abc import Callable




def  UpperCamelCase(	UpperCAmelCase_    ,			UpperCAmelCase_    ,			UpperCAmelCase_    ,			UpperCAmelCase_ = 1_00    ,			):
 UpperCAmelCase			:      Any		   =					x_start
 UpperCAmelCase			:      int		   =					fnc(UpperCAmelCase_      )
 UpperCAmelCase			:      str		   =					0.0

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

  # Increment step
  UpperCAmelCase			:      List[str]		   =					xa
  UpperCAmelCase			:      List[Any]		   =					fxa
 return area


if __name__ == "__main__":




 def  UpperCamelCase(	UpperCAmelCase_      ):
  return x**3

 print("f(x) = x^3")
 print("The area between the curve, x = -10, x = 10 and the x axis is:")
 lowercase__            =     10
 while i <= 100000:
  lowercase__            =     trapezoidal_area(f, -5, 5, i)
  print(f'''with {i} steps: {area}''')
  i *= 10




