



'''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'''





from __future__ import annotations

lowercase_	 =						[True] * 1_000_001
lowercase_	 =						2
while i * i <= 1_000_000:
  if seive[i]:
    for j in range(i * i, 1_000_001, i):
      lowercase_	 =						False
  i += 1




def lowerCAmelCase						(__A):



     """simple docstring"""



     return seive[n]




def lowerCAmelCase						(__A):



     """simple docstring"""



     return any(digit in '''02468''' for digit in str(__A))




def lowerCAmelCase						(__A = 1_000_000):



     """simple docstring"""



     _a											=						[2]  # result already includes the number 2.
     for num in range(3						,			limit + 1						,			2):
          if is_prime(__A) and not contains_an_even_digit(__A):
               _a											=						str(__A)
               _a											=						[int(str_num[j:] + str_num[:j]) for j in range(len(__A))]
               if all(is_prime(__A) for i in list_nums):
                    result.append(__A)
     return result




def lowerCAmelCase						():



     """simple docstring"""



     return len(find_circular_primes())


if __name__ == "__main__":
  print(F"""{len(find_circular_primes()) = }""")



