How can an individual believe in an omnicompetent God in a world with so much evil? Is not the problem of evil, namely belief in existence of an all-powerful, all-knowing, and all-loving God at odd with existence of such evil?

The problem of evil is undoubtedly a serious emotional barrier to a belief in an omnicompetent God, but it is rather weak, as far as I know, as an intellectual barrier. Whether in deductive form (DE), namely existence of evil is inconsistent with existence of an omnicompetent God, or inductive form (IE), existence of evil makes it improbable that an omnicompetent God exists, problems from evil are a failure as cases against existence of omnicompetent God because they assume notions that are not necessarily true.

DE, for example, assumes that if a being G is able (and knows how) to bring about not-E, willing to bring about not-E and desiring not-E, then not-E would be the case (viz., G would act accordingly to its ability, will and desire). This notion is not necessarily true, because it is possible, not necessarily true, that G has sufficiently moral justifying reason to permit E to be the case (forever or for a given period of time).

If it possibly true that a being that is able, desires and wills to bring about not-E to have morally justifying reason to permit E, then IE also assuming that some evil are seemly [as far as we know] pointless is false because as far as we know G could have sufficiently moral justifying reason to permit E.

Another often assumed notion, in DE, is that if omnipotent God cannot prevent (or eliminate) evil, then God is impotent, which is not necessarily true. A difference between God’s ability, viz., God being able to prevent evil, and God’s capability, God being capable of preventing evil, is often overlooked.

Overlooked difference between ability and capability in B can(not) do X (Morris 1991):

B can be able to but not capable of doing X. Example: I am able to cheat my wife but not capable because I dearly love my wife and also strongly believe it is immoral etc.

B can be capable of but not able to do X. Example: Adam, a mean father, is capable to physically torture her daughter, but not able because Adam is badly handicapped.

With that distinction in place, God could be able, having maximal possible power a being could have, to prevent evil but not capable. Thus God not preventing evil does not necessarily show that God lacked certain power a being could have to prevent evil.