It is demonstrated by explicit solutions of the 4+n–dimensional vacuum Einstein equations that accelerating cosmologies in the Einstein conformal frame can be obtained by a time–dependent compactification of string/M–theory, even in the case that internal dimensions are Ricci–flat, provided one includes one or more geometric twists. Such acceleration is transient. When both compact hyperbolic internal spaces and geometric twists are included, however, the period of accelerated expansion may be made arbitrarily large.