code: from __future__ import annotations
  
  from collections.abc import Callable
  def 		snake_case__  (		lowercase       ,							lowercase       ,							lowercase       ,							lowercase = 100       ,							):
     lowerCAmelCase_:       List[str]         =  x_start
     lowerCAmelCase_:       Optional[Any]         =  fnc(lowercase				)
     lowerCAmelCase_:       Optional[Any]         =  0.0
  
     for _ in range(lowercase				):
        # Approximates small segments of curve as linear and solve
        # for trapezoidal area
        lowerCAmelCase_:       str         =  (x_end - x_start) / steps + xa
        lowerCAmelCase_:       Dict         =  fnc(lowercase				)
        area += abs(fxa + fxa				) * (xa - xa) / 2
  
        # Increment step
        lowerCAmelCase_:       Any         =  xa
        lowerCAmelCase_:       Union[str, Any]         =  fxa
     return area
  
  
  if __name__ == "__main__":
   def 		snake_case__  (		lowercase				):
      return x**3
  
   print("""f(x) = x^3""")
   print("""The area between the curve, x = -10, x = 10 and the x axis is:""")
   a     :			Any					    =						1_0
   while i <= 1_0_0_0_0_0:
    a     :			Any					    =						trapezoidal_area(f, -5, 5, i)
    print(f'''with {i} steps: {area}''')
    i *= 1_0
style_context: import random
  
  class 				_lowercase						:
  
  
  
  
  
  
      '''simple docstring'''
  
  
  
  
      def __init__(						self					,	lowerCamelCase__					,	lowerCamelCase__   ):
         lowerCAmelCase_:       int         =  x
         lowerCAmelCase_:       List[str]         =  y
  
  
  
  
      def     _a						(						self   ):
         return (self.x**2 + self.y**2) <= 1
  
  
  
  
      @classmethod
      def     _a						(						cls   ):
         return cls(x=random.random()					,	y=random.random()   )
  
  
  
  
  
  def 		snake_case__  (		lowercase				):
     if number_of_simulations < 1:
        raise ValueError("At least one simulation is necessary to estimate PI."				)
  
     lowerCAmelCase_:       List[Any]         =  0
     for _ in range(lowercase				):
        lowerCAmelCase_:       Tuple         =  Point.random_unit_square()
  
        if random_point.is_in_unit_circle():
           number_in_unit_circle += 1
  
     return 4 * number_in_unit_circle / number_of_simulations
  
  
  if __name__ == "__main__":
   # import doctest
  
   # doctest.testmod()
   from math import pi
  
   a     :			Union[str, Any]					    =						"""Please enter the desired number of Monte Carlo simulations: """
   a     :			int					    =						estimate_pi(int(input(prompt).strip()))
   print(f'''An estimate of PI is {my_pi} with an error of {abs(my_pi - pi)}''')