You can give an item - claw of attack ability to a spell book and set the claw of attack ability level to x, where x is the maximum possible damage bonus achievable in your map. Hold Shift and double-click on the item's stats - Level to set to the desire level. The item ability should have an incremental bonus damage of 1.
The greater x is the greater the map loading. Anyone want to verify this, whether change is significant or not; i, certainly, notice a significant increased loading time with a 1000 level claw of attack? The increase appear to be at the 66% mark to the length of the loading bar.
Disable the spell book ability to remove the spell book icon, but still maintain the integrity of the passive bonuses.
I would advise you to use the GUI function Unit - Increase/Decrease Level of Ability for Unit. Store a unit accumulative damage in a global variable. You have to decide whether to use level 1 as 0 bonus damage or use a trigger to disable the abilities.
This method is not limited to claw of attack.
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JASS, like GUI, have no native function that add damage to a unit; no SetUnitDamage(whichUnit). You can either do as i mentioned above or used tome of damage. These are two method, in my opinion, is the most efficient.