G.R.A.P.H.

(Great Recondite Arithmetic Parabolic Helicopter) is a semi-bloon that has a "fixed survivability". It has 1000HP, and moves in TrackLength*20 px s-1. It is immune to process-disturbing (process as it moving towards exit) abilities such as distraction or freezing. It spawns nothing.

Abilities
There are 4 abilities, and is used around the middle of the track once each, while making sure that all of the abilities had their full power, and if not, an "equal power".

All attacks can't be "immuned".

3-point circle
Selects 3 towers/agents on the screen, and fires a circle such that its circumference can go through the 3 towers, dealing 12 damage to each of them.

If there is less than 3 towers/agents, the power will be condensed with higher power on each tower, while the total damage dealt must be 36. Likewise, if there is an extra tower on the circle, the damage dealt for each will be lowered.

Sine wave
Fires a red sine wave laser at 1 tower lasting for pi seconds, dealing cos(DamageTime rad)+1 damage to them. If the damaged tower dies before the finishing of this ability, it will start attacking on another, and if there are no towers left, it will stop firing, still counting the time, until another tower is placed.

The total damage must be &pi;HP.

Exponential Curve
Fires a blue sine wave laser at 2 towers lasting for 2 seconds, dealing (2*DamageTime)2*DamageTime/2 damage to them each. If the damaged tower dies before the finishing of this ability, it will start attacking on another, and if there are no towers left, it will stop firing, still counting the time, until another tower is placed.

The total damage must be $$\int^4_0{t^t \text{d}t}$$&asymp;114.1190608760432

Arbitrary Curve
Fire a green sine wave laser at 3 towers lasting for 4 seconds, dealing DamageTimeDamageTime DamageTime -1 damage each. If the damaged tower dies before the finishing of this ability, it will start attacking on another, and if there are no towers left, it will stop firing, still counting the time, until another tower is placed.

The total damage must be $$\int^4_0{t^{t^{t^{-1}}} \text{d}t}$$&asymp;12.40764930958375.

Trivia

 * Given, the Survivability is 50 DPS.
 * Given, the Firepower is 165.6683028392167 HP.
 * This is to show how a conception can't really have an accurate Firepower, or survivability, if there are resistances.