Is God's supposed omnipotence in conflict with His omni-benevolence?

This question concerns God's omnipotence (all powerful ability to do anything) and His omni-benevolence (perfect goodness). Conflict between these attributes relates to the issue of theodicy, i.e. whether these traits are compatible with the evident existence of evil within the world. The challenge is as follows: if God possesses the ability to do anything, and God has perfect benevolence, it seems that God could either prevent or remove the existence of evil within the world. Under 'evil', one can differentiate between 'moral evil', which encompasses all wrongdoing originating from human beings, and 'natural evil', which includes all the suffering and destruction that derives from nature, e.g. diseases or earthquakes. If God could prevent or remove evil, yet chooses not to do so, then it would seem that he is not perfectly good, since a perfectly good God would not allow evil to occur. If God intends to remove evil, yet cannot do so, then it would seem that He is not all powerful, since there is some logically possible thing that He cannot do. Either way, the existence of evil raises a conflict between God's omnipotence and omni-benevolence.