Work is force times the displacement in the direction of the force. In the problem that you stated, none of the directions are explicitly given. However, you state that a constant force causes the object to move at a constant speed. Therefore the constant force is zero is has a counter-acting force, so that the net force is zero. If the velocity is constant, there is NO acceleration, and therefore NO force. If work is force times displacement and there is no force, there is NO work.
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