





'''simple docstring'''


from __future__ import annotations

from collections.abc import Callable
def       __snake_case		( SCREAMING_SNAKE_CASE_ :			Callable[[int | float], int | float]			,	SCREAMING_SNAKE_CASE_ :			int | float			,	SCREAMING_SNAKE_CASE_ :			int | float			,	SCREAMING_SNAKE_CASE_ :			int = 100			,	)							->     float:

       """simple docstring"""


       UpperCAmelCase  =						x_start
       UpperCAmelCase  =						fnc(SCREAMING_SNAKE_CASE_ )
       UpperCAmelCase  =						0.0
       for _ in range(SCREAMING_SNAKE_CASE_ ):
              # Approximates small segments of curve as linear and solve
              # for trapezoidal area
              UpperCAmelCase  =						(x_end - x_start) / steps + xa
              UpperCAmelCase  =						fnc(SCREAMING_SNAKE_CASE_ )
              area += abs(fxa + fxa ) * (xa - xa) / 2
              # Increment step
              UpperCAmelCase  =						xa
              UpperCAmelCase  =						fxa
       return area


if __name__ == "__main__":
    def       __snake_case		( SCREAMING_SNAKE_CASE_ :			Optional[Any] )							->     List[str]:

           """simple docstring"""


           return x**3 + x**2

    print('f(x) = x^3 + x^2')
    print('The area between the curve, x = -5, x = 5 and the x axis is:')
    a__			:					Union[str, Any]       						=						10
    while i <= 100_000:
        print(F"""with {i} steps: {trapezoidal_area(f, -5, 5, i)}""")
        i *= 10








'''simple docstring'''


from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


_lowercase  =			{
    """configuration_pegasus_x""": ["""PEGASUS_X_PRETRAINED_CONFIG_ARCHIVE_MAP""", """PegasusXConfig"""],
}

try:
	if not is_torch_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	_lowercase  =			[
	    """PEGASUS_X_PRETRAINED_MODEL_ARCHIVE_LIST""",
	    """PegasusXForConditionalGeneration""",
	    """PegasusXModel""",
	    """PegasusXPreTrainedModel""",
	]


if TYPE_CHECKING:
	from .configuration_pegasus_x import PEGASUS_X_PRETRAINED_CONFIG_ARCHIVE_MAP, PegasusXConfig

	try:
		if not is_torch_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_pegasus_x import (
		    PEGASUS_X_PRETRAINED_MODEL_ARCHIVE_LIST,
		    PegasusXForConditionalGeneration,
		    PegasusXModel,
		    PegasusXPreTrainedModel,
		)


else:
	import sys

	_lowercase  =			_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)

