


from __future__ import annotations

import math
from collections.abc import Callable

def 	lowerCAmelCase__			(      a__:		Callable[[int | float], int | float]      ,  a__:		int | float      ,  a__:		int | float      ,  a__:		int = 1_0_0      ,  )  ->		float:


							'''simple docstring'''





							_UpperCAmelCase					=      x_start
							_UpperCAmelCase					=      fnc(a__	)
							_UpperCAmelCase					=      0.0

							for _ in range(a__	):
														# Approximates curve as a sequence of linear lines and sums their length
														_UpperCAmelCase					=      (x_end - x_start) / steps + xa
														_UpperCAmelCase					=      fnc(a__	)
														length += math.hypot(xa - xa      ,  fxa - fxa	)

														# Increment step
														_UpperCAmelCase					=      xa
														_UpperCAmelCase					=      fxa

							return length


if __name__ == "__main__":

		def 	lowerCAmelCase__			(      a__:		List[Any]	)  ->		Optional[int]:


									'''simple docstring'''





									return math.sin(1_0 * x	)

		print('''f(x) = sin(10 * x)''')
		print('''The length of the curve from x = -10 to x = 10 is:''')
		lowerCAmelCase__  :str             =							1_0
		while i <= 1_0_0_0_0_0:
				print(f'''With {i} steps: {line_length(f, -1_0, 1_0, i)}''')
				i *= 1_0




from dataclasses import dataclass
from typing import List, Optional, Union

import numpy as np
import torch

from ...utils import BaseOutput, OptionalDependencyNotAvailable, is_torch_available, is_transformers_available

@dataclass
class 		__a				(    UpperCAmelCase      ):
		_a     :  Union[List[np.ndarray], torch.FloatTensor]


try:
		if not (is_transformers_available() and is_torch_available()):
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		from ...utils.dummy_torch_and_transformers_objects import *  # noqa F403
else:
		from .pipeline_text_to_video_synth import TextToVideoSDPipeline
		from .pipeline_text_to_video_synth_imgaimg import VideoToVideoSDPipeline  # noqa: F401
		from .pipeline_text_to_video_zero import TextToVideoZeroPipeline
