



'''simple docstring'''




from collections.abc import Callable

import numpy as np



def    __lowerCamelCase						(      _lowercase			,       _lowercase			,       _lowercase			,       _lowercase			,       _lowercase	)   ->    np.array:
							UpperCAmelCase  :	Optional[Any]							  =	int(np.ceil((x_end - xa) / step_size	)	)
							UpperCAmelCase  :	str							  =	np.zeros((n + 1,)	)
							UpperCAmelCase  :	Optional[Any]							  =	ya
							UpperCAmelCase  :	Union[str, Any]							  =	xa

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

							return y


if __name__ == "__main__":
							import doctest

							doctest.testmod()






'''simple docstring'''




import math



def    __lowerCamelCase						(      _lowercase	)   ->    bool:
							assert isinstance(_lowercase			,       _lowercase	) and (
							    number >= 0
							), "'number' must been an int and positive"

							if 1 < number < 4:
														# 2 and 3 are primes
														return True
							elif number < 2 or not number % 2:
														# Negatives, 0, 1 and all even numbers are not primes
														return False

							UpperCAmelCase  :	str							  =	range(3			,       int(math.sqrt(_lowercase	) + 1	)			,       2	)
							return not any(not number % i for i in odd_numbers	)



def    __lowerCamelCase						(      _lowercase			,       _lowercase=1			,       **_lowercase	)   ->    Union[str, Any]:
							UpperCAmelCase  :	Optional[int]							  =	factor * value
							UpperCAmelCase  :	List[Any]							  =	value

							while not is_prime(_lowercase	):
														value += 1 if not ("desc" in kwargs and kwargs["desc"] is True) else -1

							if value == first_value_val:
														return next_prime(value + 1			,       **_lowercase	)
							return value

