First of all, the other two who have answered are right and please read the answers with care. The velocity of an object remains constant ONLY when there is NO NET FORCE acting on the object(Law of inertia). Hence you are wrong to think about the law of inertia when you hit the ball(i.e, apply force), aren't you?!
If we go by your thinking, applying law of inertia everywhere, there will not be any motion/change in velocity of any object, isn't it? :)
(Read the complete statement and understand it clearly before you apply it to situations)


"all the physics world problems say that a ball is thrown with a constant velocity but how can the velocity of a thrown ball have constant velocity and no acceleration if it requires a force to start it with $F = m \cdot a$?"

Now the sentence "the ball is thrown with a constant velocity" is not technically very clear and is probably the reason for your confusion.
Whoever made that statement just means that the the ball is thrown to have a certain (final)velocity which is constant after it is thrown, and the problem that you are asked to solve refers to that interval after throwing and letting it free in which the ball has a certain constant velocity (unless you again apply force on it).

You are right, you need a force to start it. The ball accelerates from rest only in the interval during which the net force on it is non-zero (the interval in which you give it a push). Once it is left free after hitting/pushing, it no more experiences any force and travels with the velocity it gained during the acceleration("final velocity"). If you need to change its velocity, you need to apply a (net non-zero) force again.

(Try to think of these experiments in free space where there is no gravitational force/air resistance etc. If your imaginations are on the earth, you are sure to go wrong because the velocity of the ball after you leave it in free air will change due to gravity/air resistance).