

import math

from numpy import inf
from scipy.integrate import quad



def 					lowerCAmelCase__							(	SCREAMING_SNAKE_CASE_:							float      )			->      float:




				'''simple docstring'''





				if num <= 0:
								raise ValueError("math domain error"      )

				return quad(SCREAMING_SNAKE_CASE_	,       0	,       SCREAMING_SNAKE_CASE_	,       args=(SCREAMING_SNAKE_CASE_)      )[0]



def 					lowerCAmelCase__							(	SCREAMING_SNAKE_CASE_:							float	,       SCREAMING_SNAKE_CASE_:							float      )			->      float:




				'''simple docstring'''





				return math.pow(SCREAMING_SNAKE_CASE_	,       z - 1      ) * math.exp(-x      )


if __name__ == "__main__":
	from doctest import testmod

	testmod()




def 					lowerCAmelCase__							(	SCREAMING_SNAKE_CASE_:							int      )			->      int:




				'''simple docstring'''





				if divisor % 5 == 0 or divisor % 2 == 0:
								return 0
				A__        =			1
				A__        =			1
				while repunit:
								A__        =			(1_0 * repunit + 1) % divisor
								repunit_index += 1
				return repunit_index



def 					lowerCAmelCase__							(	SCREAMING_SNAKE_CASE_:							int = 1_0_0_0_0_0_0      )			->      int:




				'''simple docstring'''





				A__        =			limit - 1
				if divisor % 2 == 0:
								divisor += 1
				while least_divisible_repunit(SCREAMING_SNAKE_CASE_      ) <= limit:
								divisor += 2
				return divisor


if __name__ == "__main__":
	print(f"""{solution() = }""")

