
import math

from numpy import inf
from scipy.integrate import quad


def 			UpperCamelCase					(    __lowerCamelCase     : float    ):
       if num <= 0:
              raise ValueError("math domain error"    )

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


def 			UpperCamelCase					(    __lowerCamelCase     : float				,					__lowerCamelCase     : float    ):
       return math.pow(__lowerCamelCase				,					z - 1    ) * math.exp(-x    )


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

   testmod()












'''simple docstring'''




import math
def 	UpperCAmelCase_							(					__lowercase							:      int       )		->       bool:


     '''simple docstring'''



     return math.sqrt(__lowercase       ) * math.sqrt(__lowercase       ) == num
def 	UpperCAmelCase_							(					__lowercase							:      int       )		->       bool:


     '''simple docstring'''



     _UpperCAmelCase     							=   0
     _UpperCAmelCase     							=   n
     while left <= right:
          _UpperCAmelCase     							=   (left + right) // 2
          if mid**2 == n:
               return True
          elif mid**2 > n:
               _UpperCAmelCase     							=   mid - 1
          else:
               _UpperCAmelCase     							=   mid + 1
     return False


if __name__ == "__main__":
  import doctest

  doctest.testmod()




