<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def render(self, filename=None, directory=None, view=False, cleanup=False, format=None, renderer=None, formatter=None):
 """Save the source to file and render with the Graphviz engine. Args: filename: Filename for saving the source (defaults to ``name`` + ``'.gv'``) directory: (Sub)directory for source saving and rendering. view (bool):
 Open the rendered result with the default application. cleanup (bool):
 Delete the source file after rendering. format: The output format used for rendering (``'pdf'``, ``'png'``, etc.). Returns: The (possibly relative) path of the rendered file. Raises: ValueError: If ``format``, ``renderer``, or ``formatter`` are not known. graphviz.RequiredArgumentError: If ``formatter`` is given but ``renderer`` is None. graphviz.ExecutableNotFound: If the Graphviz executable is not found. subprocess.CalledProcessError: If the exit status is non-zero. RuntimeError: If viewer opening is requested but not supported. """

        filepath = self.save(filename, directory)

        if format is None:
            format = self._format

        rendered = backend.render(self._engine, format, filepath, renderer, formatter)

        if cleanup:
            os.remove(filepath)

        if view:
            self._view(rendered, self._format)

        return rendered