



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

def 	SCREAMING_SNAKE_CASE_							(	_snake_case	:int				)  ->     Dict:

   # A local function to see if a dot lands in the circle.
   def is_in_circle(_snake_case	:float	,   _snake_case	:float				) -> bool:
      _A      =       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
   _A      =       mean(
       int(is_in_circle(uniform(-1.0	,   1.0				)	,   uniform(-1.0	,   1.0				)				)				)
       for _ in range(_snake_case				)				)
   # The ratio of the area for circle to square is pi/4.
   _A      =       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 	SCREAMING_SNAKE_CASE_							(	_snake_case	:int	,   _snake_case	:Callable[[float], float]	,   _snake_case	:float = 0.0	,   _snake_case	:float = 1.0	,   )  ->     float:
   return mean(
       function_to_integrate(uniform(_snake_case	,   _snake_case				)				) for _ in range(_snake_case				)				) * (max_value - min_value)

def 	SCREAMING_SNAKE_CASE_							(	_snake_case	:int	,   _snake_case	:float = 0.0	,   _snake_case	:float = 1.0				)  ->     None:

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

   _A      =       area_under_curve_estimator(
       _snake_case	,   _snake_case	,   _snake_case	,   _snake_case				)
   _A      =       (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 	SCREAMING_SNAKE_CASE_							(	_snake_case	:int				)  ->     None:

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

   _A      =       area_under_curve_estimator(
       _snake_case	,   _snake_case	,   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()








def 	SCREAMING_SNAKE_CASE_							(	_snake_case	:list				)  ->     bool:
   if not isinstance(_snake_case	,   _snake_case				):
      raise ValueError('''Input series is not valid, valid series - [2, 4, 6]'''				)
   if len(_snake_case				) == 0:
      raise ValueError('''Input list must be a non empty list'''				)
   if len(_snake_case				) == 1:
      return True
   _A      =       series[1] - series[0]
   for index in range(len(_snake_case				) - 1				):
      if series[index + 1] - series[index] != common_diff:
         return False
   return True

def 	SCREAMING_SNAKE_CASE_							(	_snake_case	:list				)  ->     float:
   if not isinstance(_snake_case	,   _snake_case				):
      raise ValueError('''Input series is not valid, valid series - [2, 4, 6]'''				)
   if len(_snake_case				) == 0:
      raise ValueError('''Input list must be a non empty list'''				)
   _A      =       0
   for val in series:
      answer += val
   return answer / len(_snake_case				)


if __name__ == "__main__":
   import doctest

   doctest.testmod()



