



"""simple docstring"""

def       __magic_name__    (   _lowerCamelCase				: float  ,       _lowerCamelCase				: list[float]					):
							if discount_rate < 0:
														raise ValueError("""Discount rate cannot be negative"""					)
							if not cash_flows:
														raise ValueError("""Cash flows list cannot be empty"""					)
							__a		:		Tuple									=       sum(
							    cash_flow / ((1 + discount_rate) ** i) for i, cash_flow in enumerate(_lowerCamelCase					)					)
							return round(_lowerCamelCase  ,       ndigits=2					)


if __name__ == "__main__":
	import doctest

	doctest.testmod()








"""simple docstring"""

def       __magic_name__    (   _lowerCamelCase				: int  ,       _lowerCamelCase				: float  ,       _lowerCamelCase				: float					):
							return round(float(moles / volume					) * nfactor					)





def       __magic_name__    (   _lowerCamelCase				: float  ,       _lowerCamelCase				: float  ,       _lowerCamelCase				: float					):
							return round(float((moles * 0.08_21 * temperature) / (volume)					)					)





def       __magic_name__    (   _lowerCamelCase				: float  ,       _lowerCamelCase				: float  ,       _lowerCamelCase				: float					):
							return round(float((moles * 0.08_21 * temperature) / (pressure)					)					)





def       __magic_name__    (   _lowerCamelCase				: float  ,       _lowerCamelCase				: float  ,       _lowerCamelCase				: float					):
							return round(float((pressure * volume) / (0.08_21 * moles)					)					)


if __name__ == "__main__":
	import doctest

	doctest.testmod()

