Double Strike, Trample, and Protection

[Ephraim]

If a creature with double strike and trample is blocked by a creature with protection from some quality of the attacking creature, what happens?  (Please consider both cases: attacker's power less than the blocker's toughness and attacker's power greater than or equal to the blocker's toughness.)

Thanks,
Eph

[Apollyon]

If the attacking creature has a higher power than the defending creature has toughness, you can send the difference to the opposing player for first strike and that same number for regular strike (as you need to assign lethal damage to their creature and the first strike damage to their creature does nothing).

If the attacking creature has a lower power, it deals damage twice to the defending creature.

For instance, you have a 5/5 double strike trampling green creature attacking into a 4/4 pro: green creature with no damage on it. You need to deal 4 damage to the blocker and you can choose to deal 1 damage to the player during first strike. For second strike, you still need to assign lethal. Since there is no damage on the 4/4, you need to assign another 4 to it.

Now, if that 5/5 was a 3/3, it would assign 3 to the blocker twice and deal none. For a 4/4, it would assign 4 damage twice and deal none.