





"""simple docstring"""



import math







def 						__lowercase	(  snake_case_    :    float							,snake_case_    :    float		)  ->float:



    '''simple docstring'''







    if (
        not isinstance(snake_case_							,(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 						__lowercase	(  snake_case_    :    float							,snake_case_    :    float		)  ->float:



    '''simple docstring'''







    if (
        not isinstance(snake_case_							,(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()











"""simple docstring"""



def 						__lowercase	(  snake_case_    :    list		)  ->float:



    '''simple docstring'''







    __A       :		Tuple							=	0
    while len(snake_case_		) > 1:
        __A       :		List[Any]							=	0
        # Consider two files with minimum cost to be merged
        for _ in range(2		):
            __A       :		Dict							=	files.index(min(snake_case_		)		)
            temp += files[min_index]
            files.pop(snake_case_		)
        files.append(snake_case_		)
        optimal_merge_cost += temp
    return optimal_merge_cost


if __name__ == "__main__":
       import doctest

       doctest.testmod()




