



"""simple docstring"""
from math import pow, sqrt

def       _snake_case						(						*UpperCamelCase						:		float						):
 UpperCAmelCase	:					str	=	len(UpperCamelCase						) > 0 and all(value > 0.0 for value in values						)
 return result

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

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

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

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

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





"""simple docstring"""
from collections.abc import Callable

import numpy as np

def       _snake_case						(						UpperCamelCase						:		Callable			,		UpperCamelCase						:		float			,		UpperCamelCase						:		float			,		UpperCamelCase						:		float			,		UpperCamelCase						:		float						):
 UpperCAmelCase	:					Any	=	int(np.ceil((x_end - xa) / step_size						)						)
 UpperCAmelCase	:					Optional[Any]	=	np.zeros((n + 1,)						)
 UpperCAmelCase	:					Optional[int]	=	ya
 UpperCAmelCase	:					int	=	xa

 for k in range(UpperCamelCase						):
  UpperCAmelCase	:					Optional[int]	=	y[k] + step_size * ode_func(UpperCamelCase			,		y[k]						)
  UpperCAmelCase	:					Optional[int]	=	y[k] + (
      (step_size / 2) * (ode_func(UpperCamelCase			,		y[k]						) + ode_func(x + step_size			,		UpperCamelCase						))
  )
  x += step_size

 return y


if __name__ == "__main__":
      import doctest

      doctest.testmod()
