The "problem of evil" is this:
However, that God is love and that He is all-powerful does not necessarily mean that evil and suffering would not exist in the world. There is another possible conclusion, namely, that God has a good purpose for the existence of evil and sufference.
What could this good purpose be? Well, the Bible teaches that evil and suffering result in both God's glory (in Jesus being the ultimate conquerer of evil and suffering) and greater joy for God's people (who experience firsthand God saving them from their own evil and granting them the joy of being a redeemed people who will spend eternity in heaven).
And you, who were dead in your trespasses and the uncircumcision of your flesh, God made alive together with him, having forgiven us all our trespasses, by canceling the record of debt that stood against us with its legal demands. This he set aside, nailing it to the cross. He disarmed the rulers and authorities and put them to open shame, by triumphing over them in him.
The answer given above to the "problem of evil" does not neglect the fact that there is a tremendous amount of evil and suffering in the world, and that we should feel deep empathy for those who are suffering.
However, the answer does demonstrate that the Bible is not self-contradictory regarding the "problem of evil." The idea that God's good purposes are not worth the amount of evil and suffering that exist in the world is a subjective opinion without any real justification.
If one of your objections to the Bible is the "problem of evil," where do you get your definition of evil in the first place? Christians believe that God has revealed the definition of good and evil through the Bible.
If you do not believe in God, then what is your basis for believing in good and evil in the first place? If humans are simply the product of random chance in a cold, uncaring universe where only the fittest survive, then why do you think murder, rape, and stealing are wrong?
The answer is that you are stealing principles of morality from the Christian worldview, and that you have no moral foundation to stand on when you accuse the God of the Bible as being unjust.