code: def test_pow_dtype() -> None:
      df = pl.DataFrame(
          {
              "foo": [1, 2, 3, 4, 5],
              "a": [1, 2, 3, 4, 5],
              "b": [1, 2, 3, 4, 5],
              "c": [1, 2, 3, 4, 5],
              "d": [1, 2, 3, 4, 5],
              "e": [1, 2, 3, 4, 5],
              "f": [1, 2, 3, 4, 5],
              "g": [1, 2, 1, 2, 1],
              "h": [1, 2, 1, 2, 1],
          },
          schema_overrides={
              "a": pl.Int64,
              "b": pl.UInt64,
              "c": pl.Int32,
              "d": pl.UInt32,
              "e": pl.Int16,
              "f": pl.UInt16,
              "g": pl.Int8,
              "h": pl.UInt8,
          },
      ).lazy()
  
      df = (
          df.with_columns([pl.col("foo").cast(pl.UInt32)])
          .with_columns(
              [
                  (pl.col("foo") * 2**2).alias("scaled_foo"),
                  (pl.col("foo") * 2**2.1).alias("scaled_foo2"),
                  (pl.col("a") ** pl.col("h")).alias("a_pow_h"),
                  (pl.col("b") ** pl.col("h")).alias("b_pow_h"),
                  (pl.col("c") ** pl.col("h")).alias("c_pow_h"),
                  (pl.col("d") ** pl.col("h")).alias("d_pow_h"),
                  (pl.col("e") ** pl.col("h")).alias("e_pow_h"),
                  (pl.col("f") ** pl.col("h")).alias("f_pow_h"),
                  (pl.col("g") ** pl.col("h")).alias("g_pow_h"),
                  (pl.col("h") ** pl.col("h")).alias("h_pow_h"),
              ]
          )
          .drop(["a", "b", "c", "d", "e", "f", "g", "h"])
      )
      expected = [
          pl.UInt32,
          pl.UInt32,
          pl.Float64,
          pl.Int64,
          pl.UInt64,
          pl.Int32,
          pl.UInt32,
          pl.Int16,
          pl.UInt16,
          pl.Int8,
          pl.UInt8,
      ]
      assert df.collect().dtypes == expected
      assert df.dtypes == expected
  
imports: from __future__ import annotations
  from collections import OrderedDict
  from datetime import date, timedelta
  from typing import Any, Iterator, Mapping
  import pytest
  import polars
  from polars.testing import assert_frame_equal, assert_series_equal
label_desc: Use image node_id 5 for calling a global function with example usage: test_pow_dtype() without return types