code: def integrate(
      function, initial_state, end_time=1.0, n_steps=10, step="euler"
  ):
      """Compute the flow under the vector field using symplectic euler.
  
      Integration function to compute flows of vector fields
      on a regular grid between 0 and a finite time from an initial state.
  
      Parameters
      ----------
      function : callable
          Vector field to integrate.
      initial_state : tuple of arrays
          Initial position and speed.
      end_time : float
          Final integration time.
          Optional, default : 1.
      n_steps : int
          Number of integration steps to use.
          Optional, default : 10.
      step : str, {'euler', 'rk4', 'group_rk2', 'group_rk4'}
          Numerical scheme to use for elementary integration steps.
          Optional, default : 'euler'.
  
      Returns
      -------
      final_state : tuple
          sequences of solutions every end_time / n_steps. The shape of each
          element of the sequence is the same as the vectors passed in
          initial_state.
      """
      check_parameter_accepted_values(step, "step", STEP_FUNCTIONS)
  
      dt = end_time / n_steps
      states = [initial_state]
      current_state = initial_state
  
      step_function = globals()[STEP_FUNCTIONS[step]]
  
      for i in range(n_steps):
          current_state = step_function(
              state=current_state, force=function, time=i * dt, dt=dt
          )
          states.append(current_state)
      return states
  
imports: from geomstats.errors import check_parameter_accepted_values
label_desc: Use image node_id 6 for calling a global function with example usage: integrate(function, initial_state, end_time, n_steps, step) and returns: states