Daniel,
As far as that equation goes... ?
Simply,
The reason the effects are different is due to the orientation of the wing with respect to the aircrafts centerline.

Ever stick you hand, (held flat), out a car window? With your fingers held level, call it the centerline of the airfoil, your hand is basically a airfoil.
Tilt you hand up and your hand rises.
Tilt your hand down and it drops.

Basically,
An airfoil's lift is generated by a decrease in air pressure. Change the angle of attack-the airfoils centerline with respect to the aircrafts centerline-and you'll change the lifting properties of the airfoil.
By shimming up the trailing edge of a wing you are increasing the pressure on the top of the wing and decreasing it on the bottom. I.E. you are decreasing the lift of the top of the wing and creating 'downward lift' on the bottom.
Flaps and spoilers change the shape of the trailing edge of the airfoil and not it's centerline's angle of attack nor it's original lifting ability. These control surfaces are acting like mini-airfoils-just like your hand out the car window.

I'm not employing technical terms or describing all of the forces involved; hopefully, as was the intent, it is easily understandable.

An airfoil's centerline with respect to the aircraft's centerline:
A trainer's flat-bottom, (high lift), airfoil has it's centerline some 15 degrees positive-just a guess. Thus the reason for the engine's down-thrust.
An intermediate type aircraft's airfoil, usually semi-symmetrical which creates more lift on top than on bottom, is only a few degrees positive if at all.
An experienced type aircraft's airfoil, usually fully symmetrical which creates lift equally in both directions, is also only a few degrees positive if at all.

This is just a generalization.