



'''simple docstring'''





def 						__snake_case(				_lowerCAmelCase     ,   _lowerCAmelCase		)		-> Optional[int]:
      # "extended trapezoidal rule"
      # int(f) = dx/2 * (f1 + 2f2 + ... + fn)
      snake_case__  :    int    						=      (boundary[1] - boundary[0]) / steps
      snake_case__  :    Optional[int]    						=      boundary[0]
      snake_case__  :    Tuple    						=      boundary[1]
      snake_case__  :    str    						=      make_points(_lowerCAmelCase     ,   _lowerCAmelCase     ,   _lowerCAmelCase		)
      snake_case__  :    Union[str, Any]    						=      0.0
      y += (h / 2.0) * f(_lowerCAmelCase		)
      for i in x_i:
            # print(i)
            y += h * f(_lowerCAmelCase		)
      y += (h / 2.0) * f(_lowerCAmelCase		)
      return y





def 						__snake_case(				_lowerCAmelCase     ,   _lowerCAmelCase     ,   _lowerCAmelCase		)		-> Union[str, Any]:
      snake_case__  :    Optional[Any]    						=      a + h
      while x < (b - h):
            yield x
            snake_case__  :    int    						=      x + h





def 						__snake_case(				_lowerCAmelCase		)		-> Dict:  # enter your function here
      snake_case__  :    Optional[Any]    						=      (x - 0) * (x - 0)
      return y





def 						__snake_case(				)		-> Tuple:
      snake_case__  :    Union[str, Any]    						=      0.0  # Lower bound of integration
      snake_case__  :    List[str]    						=      1.0  # Upper bound of integration
      snake_case__  :    Tuple    						=      10.0  # define number of steps or resolution
      snake_case__  :    List[str]    						=      [a, b]  # define boundary of integration
      snake_case__  :    Dict    						=      method_a(_lowerCAmelCase     ,   _lowerCAmelCase		)
      print(f"y = {y}"		)


if __name__ == "__main__":
       main()





'''simple docstring'''





__a          =		frozenset(
    [
        "prompt",
        "height",
        "width",
        "guidance_scale",
        "negative_prompt",
        "prompt_embeds",
        "negative_prompt_embeds",
        "cross_attention_kwargs",
    ]
)

__a          =		frozenset(["prompt", "negative_prompt"])

__a          =		frozenset([])

__a          =		frozenset(["image"])

__a          =		frozenset(
    [
        "image",
        "height",
        "width",
        "guidance_scale",
    ]
)

__a          =		frozenset(["image"])

__a          =		frozenset(
    [
        "prompt",
        "image",
        "height",
        "width",
        "guidance_scale",
        "negative_prompt",
        "prompt_embeds",
        "negative_prompt_embeds",
    ]
)

__a          =		frozenset(["prompt", "image", "negative_prompt"])

__a          =		frozenset(
    [
        # Text guided image variation with an image mask
        "prompt",
        "image",
        "mask_image",
        "height",
        "width",
        "guidance_scale",
        "negative_prompt",
        "prompt_embeds",
        "negative_prompt_embeds",
    ]
)

__a          =		frozenset(["prompt", "image", "mask_image", "negative_prompt"])

__a          =		frozenset(
    [
        # image variation with an image mask
        "image",
        "mask_image",
        "height",
        "width",
        "guidance_scale",
    ]
)

__a          =		frozenset(["image", "mask_image"])

__a          =		frozenset(
    [
        "example_image",
        "image",
        "mask_image",
        "height",
        "width",
        "guidance_scale",
    ]
)

__a          =		frozenset(["example_image", "image", "mask_image"])

__a          =		frozenset(["class_labels"])

__a          =		frozenset(["class_labels"])

__a          =		frozenset(["batch_size"])

__a          =		frozenset([])

__a          =		frozenset(["batch_size"])

__a          =		frozenset([])

__a          =		frozenset(
    [
        "prompt",
        "audio_length_in_s",
        "guidance_scale",
        "negative_prompt",
        "prompt_embeds",
        "negative_prompt_embeds",
        "cross_attention_kwargs",
    ]
)

__a          =		frozenset(["prompt", "negative_prompt"])
__a          =		frozenset(["input_tokens"])

__a          =		frozenset(["input_tokens"])
