code: 
  
  
  import sys
  from typing import Dict
  
  from transformers import EvalPrediction, HfArgumentParser, TrainingArguments, is_torch_available
  from transformers.utils import logging
  
  
  A_    :					List[str]             =logging.get_logger(__name__)
  
  
  if is_torch_available():
   import torch
   from torch import nn
   from torch.utils.data import Dataset
  
   from transformers import Trainer
  
  
  
  
  
   class        lowercase_				( snake_case_):
  
  
  
  
  
  
          """simple docstring"""
  
  
  
  
  
  
  
          def __init__(   self			,    _UpperCAmelCase = 101		):
  
  
  
  
  
  
  
                """simple docstring"""
  
  
                a_					=		length
  
  
          def __len__(   self		):
  
  
  
  
  
  
  
                """simple docstring"""
  
  
                return self.length
  
  
  
  
  
  
          def __getitem__(   self			,    _UpperCAmelCase		):
  
  
  
  
  
  
  
                """simple docstring"""
  
  
                return i
  
  
  
  
  
   class        lowercase_				:
  
  
  
  
  
  
          """simple docstring"""
  
  
  
  
  
  
  
          def __call__(   self			,    _UpperCAmelCase		):
  
  
  
  
  
  
  
                """simple docstring"""
  
  
                return {"input_ids": torch.tensor(_UpperCAmelCase		), "labels": torch.tensor(_UpperCAmelCase		)}
  
  
  
  
  
   class        lowercase_				( nn.Module):
  
  
  
  
  
  
          """simple docstring"""
  
  
  
  
  
  
  
          def __init__(   self		):
  
  
  
  
  
  
  
                """simple docstring"""
  
  
                super().__init__()
                # Add some (unused) params otherwise DDP will complain.
                a_					=		nn.Linear(120			,    80		)
  
  
  
  
  
  
          def 						lowercase__     (   self			,    _UpperCAmelCase			,    _UpperCAmelCase=None		):
  
  
  
  
  
  
  
                """simple docstring"""
  
  
                if labels is not None:
                      return torch.tensor(0.0			,    device=input_ids.device		), input_ids
                else:
                      return input_ids
  
  
  
  
  def   lowerCamelCase_       (					):
  
  
  
        """simple docstring"""
  
  
  
  
        a_					=		HfArgumentParser((TrainingArguments,)      )
        sys.argv += ["--output_dir", "./examples"]
        a_					=		parser.parse_args_into_dataclasses()[0]
  
        logger.warning(
            F"Process rank: {training_args.local_rank}, device: {training_args.device}, "
            F"tpu_num_cores: {training_args.tpu_num_cores}"       ,    )
  
        # Essentially, what we want to verify in the distributed case is
        # that we get all samples back, in the right order.
        # (this is crucial for prediction for instance)
        for dataset_length in [1_001, 256, 15]:
              a_					=		DummyDataset(__lowerCamelCase      )
  
              def compute_metrics(UpperCAmelCase__      ) -> Dict:
                    a_					=		list(range(len(__lowerCamelCase      )      )      )
                    a_					=		p.predictions.tolist() == sequential and p.label_ids.tolist() == sequential
                    return {"success": success}
  
              a_					=		Trainer(
                  model=DummyModel()       ,    args=__lowerCamelCase       ,    data_collator=DummyDataCollator()       ,    eval_dataset=__lowerCamelCase       ,    compute_metrics=__lowerCamelCase       ,    )
              a_					=		trainer.evaluate()
              logger.info(__lowerCamelCase      )
              if metrics["eval_success"] is not True:
                    logger.error(__lowerCamelCase      )
                    exit(1      )
  
              a_					=		trainer.predict(__lowerCamelCase      )
              logger.info(p.metrics      )
              if p.metrics["test_success"] is not True:
                    logger.error(p.metrics      )
                    exit(1      )
  
              a_					=		2
  
              a_					=		trainer.evaluate()
              logger.info(__lowerCamelCase      )
              if metrics["eval_success"] is not True:
                    logger.error(__lowerCamelCase      )
                    exit(1      )
  
              a_					=		trainer.predict(__lowerCamelCase      )
              logger.info(p.metrics      )
              if p.metrics["test_success"] is not True:
                    logger.error(p.metrics      )
                    exit(1      )
  
              a_					=		None
  
        logger.info("""🔥 All distributed tests successful"""      )
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__      ):
  
  
  
        """simple docstring"""
  
  
  
  
        main()
  
  
  if __name__ == "__main__":
   main()
style_context: 
  
  
  from collections.abc import Callable
  
  A_    :					Any             =Callable[[float], float]  # type alias for a real -> real function
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__       ,    ):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						a_					=		float(UpperCAmelCase__      )
  						while True:
  												try:
  																		a_					=		prev_guess - function(UpperCAmelCase__      ) / derivative(UpperCAmelCase__      )
  												except ZeroDivisionError:
  																		raise ZeroDivisionError("""Could not find root"""      ) from None
  												if abs(prev_guess - next_guess      ) < 10**-5:
  																		return next_guess
  												a_					=		next_guess
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__      ):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						return (x**3) - (2 * x) - 5
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__      ):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						return 3 * (x**2) - 2
  
  
  if __name__ == "__main__":
  	print(newton(f, fa, 3))