






class 					A__     :

     '''simple docstring'''






     def __init__( self      :    Optional[Any]   ,						_SCREAMING_SNAKE_CASE      :    Tuple ):






           """simple docstring"""




           UpperCamelCase					       =  n
           UpperCamelCase					       =  [None] * self.n
           UpperCamelCase					       =  0  # index of the first element
           UpperCamelCase					       =  0
           UpperCamelCase					       =  0







     def __len__( self      :    int ):






           """simple docstring"""




           return self.size







     def   _SCREAMING_SNAKE_CASE     ( self      :    Optional[Any] ):






           """simple docstring"""




           return self.size == 0







     def   _SCREAMING_SNAKE_CASE     ( self      :    str ):






           """simple docstring"""




           return False if self.is_empty() else self.array[self.front]







     def   _SCREAMING_SNAKE_CASE     ( self      :    Optional[int]   ,						_SCREAMING_SNAKE_CASE      :    Union[str, Any] ):






           """simple docstring"""




           if self.size >= self.n:
                 raise Exception('QUEUE IS FULL' )

           UpperCamelCase					       =  data
           UpperCamelCase					       =  (self.rear + 1) % self.n
           self.size += 1
           return self







     def   _SCREAMING_SNAKE_CASE     ( self      :    Optional[int] ):






           """simple docstring"""




           if self.size == 0:
                 raise Exception('UNDERFLOW' )

           UpperCamelCase					       =  self.array[self.front]
           UpperCamelCase					       =  None
           UpperCamelCase					       =  (self.front + 1) % self.n
           self.size -= 1
           return temp






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



def 			_A	(      SCREAMING_SNAKE_CASE      ):

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



def 			_A	(      SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE = 0.0	,SCREAMING_SNAKE_CASE = 1.0      ):

	def identity_function(SCREAMING_SNAKE_CASE      ) -> float:
		return x

	UpperCAmelCase__:	Tuple									= area_under_curve_estimator(
	    SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE      )
	UpperCAmelCase__:	Optional[Any]									= (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 			_A	(      SCREAMING_SNAKE_CASE      ):

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

	UpperCAmelCase__:	Union[str, Any]									= area_under_curve_estimator(
	    SCREAMING_SNAKE_CASE	,SCREAMING_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()