



'''simple docstring'''





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




def lowerCAmelCase						(__A):



     """simple docstring"""



     def is_in_circle(__A						,			__A) -> 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(__A))
     # 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 lowerCAmelCase						(__A						,			__A						,			__A = 0.0						,			__A = 1.0						,			):



     """simple docstring"""



     return mean(
         function_to_integrate(uniform(__A						,			__A)) for _ in range(__A)) * (max_value - min_value)




def lowerCAmelCase						(__A						,			__A = 0.0						,			__A = 1.0):



     """simple docstring"""



     def identity_function(__A) -> float:
          return x

     _a											=						area_under_curve_estimator(
         __A						,			__A						,			__A						,			__A)
     _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 lowerCAmelCase						(__A):



     """simple docstring"""



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

     _a											=						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()








'''simple docstring'''





def lowerCAmelCase						(__A = 1_000):



     """simple docstring"""



     _a											=						2**power
     _a											=						str(__A)
     _a											=						list(__A)
     _a											=						0

     for i in list_num:
          sum_of_num += int(__A)

     return sum_of_num


if __name__ == "__main__":
  lowercase_	 =						int(input("Enter the power of 2: ").strip())
  print("2 ^ ", power, " = ", 2**power)
  lowercase_	 =						solution(power)
  print("Sum of the digits is: ", result)



