



'''simple docstring'''




a     :    Union[str, Any]      						=					6_5_5_2_1



def    __lowerCamelCase						(      _lowercase	)   ->    int:
							UpperCAmelCase  :	str							  =	1
							UpperCAmelCase  :	Any							  =	0
							for plain_chr in plain_text:
														UpperCAmelCase  :	Optional[int]							  =	(a + ord(_lowercase	)) % MOD_ADLER
														UpperCAmelCase  :	Optional[int]							  =	(b + a) % MOD_ADLER
							return (b << 1_6) | a






'''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()

