We investigate the effect of a uniform intense terahertz radiation on hot-electron transport in semiconductors driven by a dc or slowly varying electric field of arbitrary strength. Using a vector potential for the high-frequency field and a scalar potential for the dc or slowly varying field, we are able to separate the center-of-mass motion from relative motion of electrons and to distinguish the slowly varying part from the rapidly oscillating part of the center-of-mass velocity. Considering the fact that relevant transport quantities are measured over a time interval much longer than the period of the terahertz radiation field, we obtain a set of momentum and energy balance equations, without invoking a perturbational treatment of the electron-photon interaction. These equations, which include all the multiphoton processes, are applied to the examination of hot-carrier transport in a GaAs-based quantum well subjected to a weak or a strong dc bias and irradiated by a terahertz radiation of various frequency and strength in both the parallel and vertical configurations. Up to as many as unu 550 absorption and emission multiphoton channels are included in the numerical calculation. The present approach turns out to be a very convenient and efficient tool to study the effect of an intense high-frequency radiation on dc or slowly varying carrier transport in semiconductors. Its applicable frequency range and its connection with previously developed balance-equation treatment are discussed.