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







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase      )			->     List[str]:







     def is_in_circle(__lowerCAmelCase ,   __lowerCAmelCase      ) -> bool:
          UpperCamelCase__      :       List[str]	    =  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__      :       Dict	    =  mean(
         int(is_in_circle(uniform(-1.0 ,   1.0      ) ,   uniform(-1.0 ,   1.0      )      )      )
         for _ in range(_UpperCamelCase      )      )
     # The ratio of the area for circle to square is pi/4.
     UpperCamelCase__      :       List[str]	    =  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							( __lowerCAmelCase ,   __lowerCAmelCase ,   __lowerCAmelCase = 0.0 ,   __lowerCAmelCase = 1.0 ,   )			->     float:
     return mean(
         function_to_integrate(uniform(_UpperCamelCase ,   _UpperCamelCase      )      ) for _ in range(_UpperCamelCase      )      ) * (max_value - min_value)







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase ,   __lowerCAmelCase = 0.0 ,   __lowerCAmelCase = 1.0      )			->     None:







     def identity_function(__lowerCAmelCase      ) -> float:
          return x

     UpperCamelCase__      :       Any	    =  area_under_curve_estimator(
         _UpperCamelCase ,   _UpperCamelCase ,   _UpperCamelCase ,   _UpperCamelCase      )
     UpperCamelCase__      :       int	    =  (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							( __lowerCAmelCase      )			->     None:







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

     UpperCamelCase__      :       Dict	    =  area_under_curve_estimator(
         _UpperCamelCase ,   _UpperCamelCase ,   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()







from __future__ import annotations







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase ,   __lowerCAmelCase      )			->     bool:
     if len(__lowerCAmelCase      ) == 0:
          return False
     UpperCamelCase__      :       Any	    =  len(__lowerCAmelCase      ) // 2
     if a_list[midpoint] == item:
          return True
     if item < a_list[midpoint]:
          return binary_search(a_list[:midpoint] ,   __lowerCAmelCase      )
     else:
          return binary_search(a_list[midpoint + 1 :] ,   __lowerCAmelCase      )


if __name__ == "__main__":
 lowerCamelCase     :							Any    =input('''Enter numbers separated by comma:\n''').strip()
 lowerCamelCase     :							Dict    =[int(item.strip()) for item in user_input.split(''',''')]
 lowerCamelCase     :							List[str]    =int(input('''Enter the number to be found in the list:\n''').strip())
 lowerCamelCase     :							Union[str, Any]    ='''''' if binary_search(sequence, target) else '''not '''
 print(F"""{target} was {not_str}found in {sequence}""")