


import math

from numpy import inf
from scipy.integrate import quad


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

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


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


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

						testmod()




import inspect
import unittest







class  snake_case__(							unittest.TestCase							):







						'''simple docstring'''




						def   lowercase_       ( self							)    ->			int:
										try:
														import diffusers  # noqa: F401
										except ImportError:
														assert False




						def   lowercase_       ( self							)    ->			List[str]:
										import diffusers
										from diffusers.dependency_versions_table import deps

										lowerCAmelCase_       :					Any			 = inspect.getmembers(__lowercase      ,  inspect.isclass							)

										for cls_name, cls_module in all_classes:
														if "dummy_" in cls_module.__module__:
																		for backend in cls_module._backends:
																						if backend == "k_diffusion":
																										lowerCAmelCase_       :					Optional[int]			 = '''k-diffusion'''
																						elif backend == "invisible_watermark":
																										lowerCAmelCase_       :					Dict			 = '''invisible-watermark'''
																						assert backend in deps, f"""{backend} is not in the deps table!"""