

'''simple docstring'''




_lowercase		:				Dict	       =		[
    "VerificationMode",
    "Version",
    "disable_progress_bar",
    "enable_progress_bar",
    "is_progress_bar_enabled",
    "experimental",
]

from .info_utils import VerificationMode
from .logging import disable_progress_bar, enable_progress_bar, is_progress_bar_enabled
from .version import Version
from .experimental import experimental






'''simple docstring'''




from collections.abc import Callable

import numpy as np




def 							lowerCamelCase			(   UpperCAmelCase__ :      Callable   ,   UpperCAmelCase__ :      float   ,   UpperCAmelCase__ :      float   ,   UpperCAmelCase__ :      float   ,   UpperCAmelCase__ :      float				)    ->   np.array:
							lowercase_      :    Any       		= int(np.ceil((x_end - xa) / step_size				)				)
							lowercase_      :    List[Any]       		= np.zeros((n + 1,)				)
							lowercase_      :    List[Any]       		= ya
							lowercase_      :    List[str]       		= xa

							for k in range(UpperCAmelCase__				):
														lowercase_      :    Optional[Any]       		= y[k] + step_size * ode_func(UpperCAmelCase__   ,   y[k]				)
														lowercase_      :    List[Any]       		= 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()





