





def 			SCREAMING_SNAKE_CASE__     (					_lowercase    :   Union[str, Any]      ,						_lowercase    :   Optional[int] )      ->       Dict:




		'''simple docstring'''
		# "Simpson Rule"
		# int(f) = delta_x/2 * (b-a)/3*(f1 + 4f2 + 2f_3 + ... + fn)
		lowercase__				:			Union[str, Any]            =		(boundary[1] - boundary[0]) / steps
		lowercase__				:			Optional[Any]            =		boundary[0]
		lowercase__				:			Any            =		boundary[1]
		lowercase__				:			Optional[Any]            =		make_points(_lowercase      ,						_lowercase      ,						_lowercase )
		lowercase__				:			Any            =		0.0
		y += (h / 3.0) * f(_lowercase )
		lowercase__				:			List[str]            =		2
		for i in x_i:
				y += (h / 3) * (4 - 2 * (cnt % 2)) * f(_lowercase )
				cnt += 1
		y += (h / 3.0) * f(_lowercase )
		return y


def 			SCREAMING_SNAKE_CASE__     (					_lowercase    :   int      ,						_lowercase    :   str      ,						_lowercase    :   List[str] )      ->       List[Any]:




		'''simple docstring'''
		lowercase__				:			Dict            =		a + h
		while x < (b - h):
				yield x
				lowercase__				:			Tuple            =		x + h


def 			SCREAMING_SNAKE_CASE__     (					_lowercase    :   Any )      ->       Any:  # enter your function here




		'''simple docstring'''
		lowercase__				:			Dict            =		(x - 0) * (x - 0)
		return y


def 			SCREAMING_SNAKE_CASE__     (					)      ->       str:




		'''simple docstring'''
		lowercase__				:			Optional[Any]            =		0.0  # Lower bound of integration
		lowercase__				:			List[str]            =		1.0  # Upper bound of integration
		lowercase__				:			List[str]            =		10.0  # define number of steps or resolution
		lowercase__				:			Union[str, Any]            =		[a, b]  # define boundary of integration
		lowercase__				:			Dict            =		method_a(_lowercase      ,						_lowercase )
		print(f"""y = {y}""" )


if __name__ == "__main__":
			main()









from typing import List

import PIL
import torch
from PIL import Image

from ...configuration_utils import ConfigMixin
from ...models.modeling_utils import ModelMixin
from ...utils import PIL_INTERPOLATION


class 			__lowerCAmelCase				(					_UpperCamelCase      ,						_UpperCamelCase			):


	'''simple docstring'''





	def __init__(	self:	Union[str, Any] ):
			super().__init__()

			self.register_buffer('watermark_image',				torch.zeros((62, 62, 4) ) )
			lowercase__				:			int            =		None





	def       snake_case__(	self:	Optional[int],				lowerCamelCase_:	List[PIL.Image.Image],				lowerCamelCase_:	Dict=None ):
			# copied from https://github.com/deep-floyd/IF/blob/b77482e36ca2031cb94dbca1001fc1e6400bf4ab/deepfloyd_if/modules/base.py#L287

			lowercase__				:			str            =		images[0].height
			lowercase__				:			Optional[Any]            =		images[0].width

			lowercase__				:			List[Any]            =		sample_size or h

			lowercase__				:			Any            =		min(h / sample_size,				w / sample_size )
			lowercase__      ,							lowercase__				:			Optional[int]            =		(int(h / coef ), int(w / coef )) if coef < 1 else (h, w)

			lowercase__      ,							lowercase__				:			Any            =		1024**2, img_w * img_h
			lowercase__				:			Union[str, Any]            =		(Sa / Sa) ** 0.5
			lowercase__      ,							lowercase__      ,							lowercase__				:			Optional[int]            =		int(K * 62 ), img_w - int(14 * K ), img_h - int(14 * K )

			if self.watermark_image_as_pil is None:
					lowercase__				:			Tuple            =		self.watermark_image.to(torch.uinta ).cpu().numpy()
					lowercase__				:			str            =		Image.fromarray(lowerCamelCase_,				mode='RGBA' )
					lowercase__				:			Tuple            =		watermark_image

			lowercase__				:			Optional[int]            =		self.watermark_image_as_pil.resize(
			    (wm_size, wm_size),				PIL_INTERPOLATION['bicubic'],				reducing_gap=lowerCamelCase_ )

			for pil_img in images:
					pil_img.paste(lowerCamelCase_,				box=(wm_x - wm_size, wm_y - wm_size, wm_x, wm_y),				mask=wm_img.split()[-1] )

			return images


