

'''simple docstring'''





def 							_lowerCAmelCase (      __magic_name__	:    int      ,   __magic_name__	:    int	)							->     Optional[int]:


						if a < 0 or b < 0:
												raise ValueError('''the value of both inputs must be positive'''	)

						lowercase   :       Optional[int]								=str(bin(_lowerCamelCase	)	)[2:]  # remove the leading "0b"
						lowercase   :       Optional[int]								=str(bin(_lowerCamelCase	)	)[2:]  # remove the leading "0b"

						lowercase   :       Optional[int]								=max(len(_lowerCamelCase	)      ,   len(_lowerCamelCase	)	)

						return "0b" + "".join(
						    str(int(char_a != char_b	)	)
						    for char_a, char_b in zip(a_binary.zfill(_lowerCamelCase	)      ,   b_binary.zfill(_lowerCamelCase	)	)	)


if __name__ == "__main__":
							import doctest

							doctest.testmod()








'''simple docstring'''





import math






def 							_lowerCAmelCase (      __magic_name__	:    float      ,   __magic_name__	:    float	)							->     float:
						if (
						    not isinstance(__magic_name__      ,   (int, float)	)
						    or power_factor < -1
						    or power_factor > 1
						):
												raise ValueError('''power_factor must be a valid float value between -1 and 1.'''	)
						return apparent_power * power_factor






def 							_lowerCAmelCase (      __magic_name__	:    float      ,   __magic_name__	:    float	)							->     float:
						if (
						    not isinstance(__magic_name__      ,   (int, float)	)
						    or power_factor < -1
						    or power_factor > 1
						):
												raise ValueError('''power_factor must be a valid float value between -1 and 1.'''	)
						return apparent_power * math.sqrt(1 - power_factor**2	)


if __name__ == "__main__":
							import doctest

							doctest.testmod()





