  We discuss a possible compactification of a higher-dimensional gravitational
theory, which give rise to a de Sitter or an accelerating universe, to the
extent that it can describe a low energy limit of string theory. Such analysis
can be carried out by the usual integration over the internal space in the
Einstein equations. The combined field equations in the higher-dimensional
supergravity theory after integration give several new terms which may help to
realize a de Sitter compactification. After developing the general framework,
we describe some specific examples involving the dilaton and mass parameter.
