from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean




def       __lowerCAmelCase      (						A_   : int					)    ->  str:

  # A local function to see if a dot lands in the circle.
  def is_in_circle(A_   : float						,	A_   : float					) -> bool:
    __UpperCAmelCase						    =       sqrt((x**2) + (y**2)					)
    # Our circle has a radius of 1, so a distance
    # greater than 1 would land outside the circle.
    return distance_from_centre <= 1

  # The proportion of guesses that landed in the circle
  __UpperCAmelCase						    =       mean(
      int(is_in_circle(uniform(-1.0						,	1.0					)						,	uniform(-1.0						,	1.0					)					)					)
      for _ in range(A_					)					)
  # The ratio of the area for circle to square is pi/4.
  __UpperCAmelCase						    =       proportion * 4
  print(F'''The estimated value of pi is {pi_estimate}'''					)
  print(F'''The numpy value of pi is {pi}'''					)
  print(F'''The total error is {abs(pi - pi_estimate					)}'''					)




def       __lowerCAmelCase      (						A_   : int						,	A_   : Callable[[float], float]						,	A_   : float = 0.0						,	A_   : float = 1.0						,	)    ->  float:
  return mean(
      function_to_integrate(uniform(A_						,	A_					)					) for _ in range(A_					)					) * (max_value - min_value)




def       __lowerCAmelCase      (						A_   : int						,	A_   : float = 0.0						,	A_   : float = 1.0					)    ->  None:

  def identity_function(A_   : float					) -> float:
    return x

  __UpperCAmelCase						    =       area_under_curve_estimator(
      A_						,	A_						,	A_						,	A_					)
  __UpperCAmelCase						    =       (max_value * max_value - min_value * min_value) / 2

  print("******************"					)
  print(F'''Estimating area under y=x where x varies from {min_value} to {max_value}'''					)
  print(F'''Estimated value is {estimated_value}'''					)
  print(F'''Expected value is {expected_value}'''					)
  print(F'''Total error is {abs(estimated_value - expected_value					)}'''					)
  print("******************"					)




def       __lowerCAmelCase      (						A_   : int					)    ->  None:

  def function_to_integrate(A_   : float					) -> float:
    return sqrt(4.0 - x * x					)

  __UpperCAmelCase						    =       area_under_curve_estimator(
      A_						,	A_						,	0.0						,	2.0					)

  print("******************"					)
  print("Estimating pi using area_under_curve_estimator"					)
  print(F'''Estimated value is {estimated_value}'''					)
  print(F'''Expected value is {pi}'''					)
  print(F'''Total error is {abs(estimated_value - pi					)}'''					)
  print("******************"					)


if __name__ == "__main__":
       import doctest

       doctest.testmod()




import copy
from dataclasses import dataclass
from pathlib import Path
from typing import Dict, Optional, Union


@dataclass
class 			UpperCAmelCase__    :



  """simple docstring"""






  lowerCAmelCase__		:	Optional[Union[str, Path]]    		= None
  lowerCAmelCase__		:	bool    		= False
  lowerCAmelCase__		:	bool    		= False
  lowerCAmelCase__		:	bool    		= False
  lowerCAmelCase__		:	Optional[Dict]    		= None
  lowerCAmelCase__		:	Optional[str]    		= None
  lowerCAmelCase__		:	bool    		= False
  lowerCAmelCase__		:	bool    		= False
  lowerCAmelCase__		:	bool    		= False
  lowerCAmelCase__		:	bool    		= True
  lowerCAmelCase__		:	Optional[int]    		= None
  lowerCAmelCase__		:	int    		= 1
  lowerCAmelCase__		:	Optional[Union[str, bool]]    		= None
  lowerCAmelCase__		:	bool    		= False
  lowerCAmelCase__		:	Optional[Dict]    		= None
  lowerCAmelCase__		:	Optional[str]    		= None






  def 	_UpperCAmelCase				(				self:			Any   ) -> "DownloadConfig":




    '''simple docstring'''




    return self.__class__(**{k: copy.deepcopy(__lowerCAmelCase   ) for k, v in self.__dict__.items()}   )



