from __future__ import annotations

from collections.abc import Callable
def 					_snake_case	(  __snake_case  ,     __snake_case  ,     __snake_case  ,     __snake_case = 100  ,     ):
					_UpperCamelCase			     =     x_start
					_UpperCamelCase			     =     fnc(__snake_case						)
					_UpperCamelCase			     =     0.0
					for _ in range(__snake_case						):
										# Approximates small segments of curve as linear and solve
										# for trapezoidal area
										_UpperCamelCase			     =     (x_end - x_start) / steps + xa
										_UpperCamelCase			     =     fnc(__snake_case						)
										area += abs(fxa + fxa						) * (xa - xa) / 2
										# Increment step
										_UpperCamelCase			     =     xa
										_UpperCamelCase			     =     fxa
					return area


if __name__ == "__main__":
					def 					_snake_case	(  __snake_case						):
										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:")
					_lowerCAmelCase       =		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_flax_available,
    is_tf_available,
    is_torch_available,
)


lowercase__						       =      {"configuration_encoder_decoder": ["EncoderDecoderConfig"]}

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowercase__						       =      ["EncoderDecoderModel"]

try:
						if not is_tf_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowercase__						       =      ["TFEncoderDecoderModel"]

try:
						if not is_flax_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowercase__						       =      ["FlaxEncoderDecoderModel"]

if TYPE_CHECKING:
						from .configuration_encoder_decoder import EncoderDecoderConfig

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_encoder_decoder import EncoderDecoderModel

						try:
												if not is_tf_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_tf_encoder_decoder import TFEncoderDecoderModel

						try:
												if not is_flax_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_flax_encoder_decoder import FlaxEncoderDecoderModel

else:
						import sys

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


