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
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)}''')