






import math

from numpy import inf
from scipy.integrate import quad





def 	lowerCAmelCase_		(lowercase__						:       float       )		->    float:


				'''simple docstring'''




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

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





def 	lowerCAmelCase_		(lowercase__						:       float     ,					lowercase__						:       float       )		->    float:


				'''simple docstring'''




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


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

			testmod()













from __future__ import annotations





def 	lowerCAmelCase_		(lowercase__						:       list[int]       )		->    bool:


				'''simple docstring'''




				return len(set(lowercase__       )       ) == len(lowercase__       )


if __name__ == "__main__":
			import doctest

			doctest.testmod()





