code: def test_windowed_groupby_aggs_with_start_state(stream):
      example = cudf.DataFrame({"name": [], "amount": []})
      sdf = DataFrame(stream, example=example)
      output0 = (
          sdf.window(5, with_state=True, start=None)
          .groupby(["name"])
          .amount.sum()
          .stream.gather()
          .sink_to_list()
      )
  
      df = cudf.DataFrame(
          {"name": ["Alice", "Tom", "Linda"], "amount": [50, 100, 200]}
      )
      stream.emit(df)
      df = cudf.DataFrame(
          {"name": ["Alice", "Linda", "Bob"], "amount": [250, 300, 350]}
      )
      stream.emit(df)
  
      stream = Stream()
      example = cudf.DataFrame({"name": [], "amount": []})
      sdf = DataFrame(stream, example=example)
      output1 = (
          sdf.window(5, with_state=True, start=output0[-1][0])
          .groupby(["name"])
          .amount.sum()
          .stream.gather()
          .sink_to_list()
      )
      df = cudf.DataFrame(
          {
              "name": ["Alice", "Linda", "Tom", "Bob"],
              "amount": [50, 100, 150, 200],
          }
      )
      stream.emit(df)
      out_df1 = cudf.DataFrame(
          {
              "name": ["Alice", "Bob", "Linda", "Tom"],
              "amount": [50, 550, 100, 150],
          }
      )
      assert_eq(output1[-1][1].reset_index(), out_df1)
  
imports: import json
  import operator
  import numpy
  import pandas
  import pytest
  from dask.dataframe.utils import assert_eq
  from distributed import Client
  from streamz import Stream
  from streamz.dask import DaskStream
  from streamz.dataframe import Aggregation, DataFrame, DataFrames, Series
label_desc: Use image node_id 42 for calling a global function with example usage: test_windowed_groupby_aggs_with_start_state(stream) without return types