




from math import pow, sqrt




def 		lowerCAmelCase_   (	*lowerCamelCase   ):
				__magic_name__	:	Tuple								=len(lowerCamelCase   ) > 0 and all(value > 0.0 for value in values   )
				return result




def 		lowerCAmelCase_   (	lowerCamelCase	,     lowerCamelCase   ):
				return (
				    round(sqrt(molar_mass_a / molar_mass_a   )	,     6   )
				    if validate(lowerCamelCase	,     lowerCamelCase   )
				    else ValueError("""Input Error: Molar mass values must greater than 0."""   )
				)




def 		lowerCAmelCase_   (	lowerCamelCase	,     lowerCamelCase	,     lowerCamelCase   ):
				return (
				    round(effusion_rate * sqrt(molar_mass_a / molar_mass_a   )	,     6   )
				    if validate(lowerCamelCase	,     lowerCamelCase	,     lowerCamelCase   )
				    else ValueError(
				        """Input Error: Molar mass and effusion rate values must greater than 0."""   )
				)




def 		lowerCAmelCase_   (	lowerCamelCase	,     lowerCamelCase	,     lowerCamelCase   ):
				return (
				    round(effusion_rate / sqrt(molar_mass_a / molar_mass_a   )	,     6   )
				    if validate(lowerCamelCase	,     lowerCamelCase	,     lowerCamelCase   )
				    else ValueError(
				        """Input Error: Molar mass and effusion rate values must greater than 0."""   )
				)




def 		lowerCAmelCase_   (	lowerCamelCase	,     lowerCamelCase	,     lowerCamelCase   ):
				return (
				    round(molar_mass / pow(effusion_rate_a / effusion_rate_a	,     2   )	,     6   )
				    if validate(lowerCamelCase	,     lowerCamelCase	,     lowerCamelCase   )
				    else ValueError(
				        """Input Error: Molar mass and effusion rate values must greater than 0."""   )
				)




def 		lowerCAmelCase_   (	lowerCamelCase	,     lowerCamelCase	,     lowerCamelCase   ):
				return (
				    round(pow(effusion_rate_a / effusion_rate_a	,     2   ) / molar_mass	,     6   )
				    if validate(lowerCamelCase	,     lowerCamelCase	,     lowerCamelCase   )
				    else ValueError(
				        """Input Error: Molar mass and effusion rate values must greater than 0."""   )
				)










from math import atan, cos, radians, sin, tan

from .haversine_distance import haversine_distance

UpperCAmelCase_		:				Dict									=     637_8137.0
UpperCAmelCase_		:				List[Any]									=     635_6752.31_4245
UpperCAmelCase_		:				List[str]									=     6378137




def 		lowerCAmelCase_   (	lowerCamelCase	,     lowerCamelCase	,     lowerCamelCase	,     lowerCamelCase   ):
				__magic_name__	:	str								=(AXIS_A - AXIS_B) / AXIS_A
				# Parametric latitudes
				# https://en.wikipedia.org/wiki/Latitude#Parametric_(or_reduced)_latitude
				__magic_name__	:	str								=atan((1 - flattening) * tan(radians(lowerCamelCase   )   )   )
				__magic_name__	:	List[Any]								=atan((1 - flattening) * tan(radians(lowerCamelCase   )   )   )

				# Compute central angle between two points
				# using haversine theta. sigma =  haversine_distance / equatorial radius
				__magic_name__	:	List[Any]								=haversine_distance(lowerCamelCase	,     lowerCamelCase	,     lowerCamelCase	,     lowerCamelCase   ) / EQUATORIAL_RADIUS

				# Intermediate P and Q values
				__magic_name__	:	Tuple								=(b_lata + b_lata) / 2
				__magic_name__	:	int								=(b_lata - b_lata) / 2

				# Intermediate X value
				# X = (sigma - sin(sigma)) * sin^2Pcos^2Q / cos^2(sigma/2)
				__magic_name__	:	Optional[int]								=(sin(lowerCamelCase   ) ** 2) * (cos(lowerCamelCase   ) ** 2)
				__magic_name__	:	Any								=cos(sigma / 2   ) ** 2
				__magic_name__	:	List[Any]								=(sigma - sin(lowerCamelCase   )) * (x_numerator / x_demonimator)

				# Intermediate Y value
				# Y = (sigma + sin(sigma)) * cos^2Psin^2Q / sin^2(sigma/2)
				__magic_name__	:	Any								=(cos(lowerCamelCase   ) ** 2) * (sin(lowerCamelCase   ) ** 2)
				__magic_name__	:	Optional[Any]								=sin(sigma / 2   ) ** 2
				__magic_name__	:	str								=(sigma + sin(lowerCamelCase   )) * (y_numerator / y_denominator)

				return EQUATORIAL_RADIUS * (sigma - ((flattening / 2) * (x_value + y_value)))


if __name__ == "__main__":
							import doctest

							doctest.testmod()




