The rods soak up neutrons. the reactor is designed so that its power would increase if the rods weren't there. The rods are what keeps the k == 1 (basically how the neutrons change in time. K == 1 is no change).
So don't think of the rods as a throttle valve in your car, i.e. this throttle angle corresponds to this much torque and therefore power. The rods are best thought of as controlling the rate of change of reactor power.
This is why the reactor is built so that the neutrons increase when fully withdrawn - because you have to start it! If the reactor is being started, the rods are withdrawn until the power wanted is achieved. Then the rods are lowered.
Note this is a far more complicated problem; this is a very serious operation because at the very start, except for your neutron starter, you only have "prompt" neutrons that can very quickly cause an increase of power. Once the reactor has stabilized the "nuclear waste" inside it releases non-prompt neutrons that are part of the neutron budget and are easier to control.
So, while waste in the reactor is being accumulated and while the fuel burns up, the position of the rods to achieve stable power changes! Furthermore these changes are different in different parts of the reactor so each rod is individually changed (actually I think there are two sets of rods, not all of them are individually actuated)