code: def _coerce_to_type(x: Index) -> tuple[Index, DtypeObj | None]:
      """
      if the passed data is of datetime/timedelta, bool or nullable int type,
      this method converts it to numeric so that cut or qcut method can
      handle it
      """
      dtype: DtypeObj | None = None
  
      if _is_dt_or_td(x.dtype):
          dtype = x.dtype
      elif is_bool_dtype(x.dtype):
          # GH 20303
          x = x.astype(np.int64)
      # To support cut and qcut for IntegerArray we convert to float dtype.
      # Will properly support in the future.
      # https://github.com/pandas-dev/pandas/pull/31290
      # https://github.com/pandas-dev/pandas/issues/31389
      elif isinstance(x.dtype, ExtensionDtype) and is_numeric_dtype(
          x.dtype
      ):
          x_arr = x.to_numpy(dtype=np.float64, na_value=np.nan)
          x = Index(x_arr)
  
      return Index(x), dtype
  
imports: from __future__ import annotations
  from typing import TYPE_CHECKING, Any, Callable, Literal
  import numpy
  from pandas._libs import Timedelta, Timestamp, lib
  from pandas.core.dtypes.common import ensure_platform_int, is_bool_dtype, is_integer, is_list_like, is_numeric_dtype, is_scalar
  from pandas.core.dtypes.dtypes import CategoricalDtype, DatetimeTZDtype, ExtensionDtype
  from pandas.core.dtypes.generic import ABCSeries
  from pandas.core.dtypes.missing import isna
  from pandas import Categorical, Index, IntervalIndex
  import pandas.core.algorithms
  from pandas.core.arrays.datetimelike import dtype_to_unit
label_desc: Use image node_id 5 for calling a global function with example usage: _coerce_to_type(x) and returns: Index,  dtype