code: def test_groupby_apply_with_df_or_series_output(setup):
      raw = pd.DataFrame(
          {
              "a": [3, 4, 5, 3, 5, 4, 1, 2, 3],
              "b": [6, 3, 3, 5, 6, 5, 4, 4, 4],
              "c": list("aabaabbbb"),
          }
      )
      mdf = md.DataFrame(raw, chunk_size=3)
  
      def f1(df):
          return df.a.iloc[2]
  
      with pytest.raises(TypeError):
          mdf.groupby("c").apply(f1)
  
      with pytest.raises(ValueError):
          mdf.groupby("c").apply(
              f1, output_types=["df_or_series"]
          ).execute()
  
      for kwargs in [
          dict(output_type="df_or_series"),
          dict(skip_infer=True),
      ]:
          mdf = md.DataFrame(raw, chunk_size=5)
          applied = mdf.groupby("c").apply(f1, **kwargs)
          assert isinstance(applied, DATAFRAME_OR_SERIES_TYPE)
          applied = applied.execute()
          assert applied.data_type == "series"
          assert not ("dtypes" in applied.data_params)
          assert applied.shape == (2,)
          pd.testing.assert_series_equal(
              applied.fetch().sort_index(),
              raw.groupby("c").apply(f1).sort_index(),
          )
  
      def f2(df):
          return df[["a"]]
  
      mdf = md.DataFrame(raw, chunk_size=5)
      applied = mdf.groupby("c").apply(
          f2, output_types=["df_or_series"]
      )
      assert isinstance(applied, DATAFRAME_OR_SERIES_TYPE)
      applied = applied.execute()
      assert applied.data_type == "dataframe"
      assert not ("dtype" in applied.data_params)
      assert applied.shape == (9, 1)
      expected = raw.groupby("c", as_index=True).apply(f2)
      pd.testing.assert_series_equal(applied.dtypes, expected.dtypes)
      pd.testing.assert_frame_equal(
          applied.fetch().sort_index(), expected.sort_index()
      )
  
imports: from collections import OrderedDict
  import numpy
  import pandas
  import pytest
  from ....None import dataframe
  from ....config import option_context
  from ....core.operand import OperandStage
  from ....tests.core import assert_groupby_equal, require_cudf
  from ....utils import arrow_array_to_objects, pd_release_version
  from ...core import DATAFRAME_OR_SERIES_TYPE
  from ..aggregation import DataFrameGroupByAgg
label_desc: Use image node_id 11 for calling a global function with example usage: test_groupby_apply_with_df_or_series_output(setup) and returns: df, df