Since there is a reliable derivative, a method of integration should also be considered.
The accumulation of Cuil as time progresses:
∫ t‽ dt
So that you can measure the amount of Cuil that is abstracted (or created? I don't know how Cuil is formed) from reality into surreality. This would have many more applications than simply differentiation; since you can refer to the level of Cuil that occurs without being part of or manipulating the function of Cuil in itself.
You walk into a gas station to buy a candy bar. The manager walks toward you, and you begin to think that Saturday would have been a good day to stay home. You pick up the candy bar, only to realize your clothes have turned into a Twix wrapper. The manager; as he gnaws on your caramel-crunchy-cookie center, informs you that if you want to purchase something, you must first inform the bar that is hiding in your clothes to wait outside. You; ashamed of what this chocolate is doing to your hips, return to your box and wait for Monday to come.
(Note: This is a similar function of ‽ as Noria's in that the original reality is reversed from perspective of consumer to product; this was intentional in order to correlate the idea of integration to differentiation.)
The ∫ t‽ dt of this would then be equal to the amount of Cuil which occurs in the situation. Since it can be observed that Cuil theory usually applies to individual situations; there will always be a finite amount of time; and therefore, a limited domain. Cuil usually occurs in integers, so this means that we can estimate the accumulation to a fairly accurate degree; using geometric representations of area.
The level of Cuil sustained for each increment of time is multiplied and then repeated to each level obtained within the function.
This would give us an estimate of the accumulation of Cuil for each situation presented; which could possibly have applications to 'scoring' Cuil theory.