Was there a sacrifice in the Old Testament for intentional sins?

To suggest that all sin, both intential and not were not forgiven after a proper sacrifice was offered, simply because the word, "intential" is not used, places the forgiving power of God at odds with His mercy. Remember, the word, "trinity" is not found in scripture yet it exists.
On another note-the comment made that the sacrifices of the ot were useless is just a total misunderstanding of scripture. To say they only pointed toward Christ ia again another misunderstanding of scripture. There is a clear and present lack of theological understanding on your part. You strive to show yourself knowledgeable by quoting passages but your logic is flawed. Be blessed and rethink your theology for the good of yourself and others.

The sin and trespass offerings used only for sins of ignorance make me feel hopeless. Indeed, Israel went through 10 cycles of falling away and being rescued by God during the 300 years of the judges just after Moses' time. The only hint that God would forgive intentional sin in the trespass offering is in Lev. 6:1-5 and then it only covers lying and steeling. It is ironic that God had chosen a murderer (Moses) to document this and murder isn't mentioned here. Heb. 10 tells us if we sin willfully after receiving a knowledge of the truth, there no longer remains a sacrifice for us. Heb. 6 says if we fall away after being partakers of the Holy Spirit, it is impossible to repent. Things I have read in this article and studied in the sacrifices that cover only sins of ignorance make the human race seem hopeless.
However, Jesus is our High Priest. He has His high Priests garments, each of which represents atonement for specific types of sins: Arrogance, errors in judgment, sins of the heart, idolatry, evil speech, killing and sexual sin. Christ overcame in all points. He came to seek and save the lost. He forgave the adulteress, the tax collector Zacheus and the thief on the cross. He cast demons out of totally possessed people. These people were involved and delivered from intentional sin. Christ gave the story of the prodigal son who was welcomed by His Father with open arms when he returned. He came to seek and save the lost and gave Himself as the Sacrifice. Heb 10:14 "For by one offering He has perfected forever those who are being sanctified". Sanctification is the work of a lifetime. He wants us to live without sin but if we stumble, He wants us to repent. "My little children, these things I write to you, so that you may not sin. And if anyone sins, we have an Advocate with the Father, Jesus Christ the righteous. And He Himself is the propitiation for our sins..." 1 John, 2:1-2.
In Jesus, there is hope.

I do believe that the context in which these sacrifices were given needs to be strongly considered. When God gave Moses the design for the tabernacle beginning in Exodus 25, Israel had just signed onto the Mosaic covenant "All that the Lord has said we will do." Israel had now been turned from a people into a nation with a constitution to which the citizens had given attestation. Laws had been laid out in chapters 20-24, which now required adherence because of the people's impetuous response.

God, knowing the nature of man, anticipated the people's inability to keep what they had just promised. So He provided a provision for when the people would break this Constitution. And the Constitution was necessary for maintaining law and order in this nation.

John Adams, concerning the US Constitution, was quoted as saying "Our Constitution was made only for a moral and religious people. It is wholly inadequate to the government of any other". I hold that what applied to Adams' attitude concerning the US Constitution, applies very much to the law of Moses.

This new wilderness wandering nation, Israel, could only succeed if it were "moral and religious". The morality was found in the dos and don'ts of the law. The "religion" was dependent upon a universal recognition of the nature of this God who made up this law as well as an appreciation for both His justice and the utter depth of His mercy provided by the intricate and solemn details of the Tabernacle and the sacrificial system. Only such a people would maintain a national cohesiveness!

Hence, intentional breaking of this law, was, as the first contributor pointed out, an act of sedition or mutiny. It was not only an affront to God but an attack on the very fabric of the nation, and could not be allowed (as that was the very nature of the Adversarys (Satan's) attack on the kingdom of God). Hence, the sacrificial system provided no provision for such an act.

In Jeremiah 31, because of Israel's consistent breaking of the Constitution, God signed a certificate of divorce to the nation (not the people - i.e. "I will make a new covenant with the house of David..." but the nation). Israel lost its autonomy as a nation. It fell into the hands of the Babylonians, Greeks, etc. and never gained back its autonomy until 1948. In light of that the Mosaic Constitution lost its relevance. In particular, no longer were the people required to be faithful to the Constitution of the nation of Israel, but to those elements which were moral within the Constitutions of the lands to which they'd been scattered. Those constitutions were imperfect, unlike the Mosaic Constitution, and provided literal discouragement towards keeping the Mosaic law concerning Sabbath worship, keeping of dietary laws, etc. In many cases, intentional sin would now become the norm within a culture in contrast to righteousness as was intended to be the norm in ancient Israel. But, even as God had provided the tabernacle for provision of sin, God did provide a better provision... Jesus. The genuine believer in Jesus, however, must now think of himself as a member of a new nation or family and his endeavors should be with the intent of enabling that nation/family to thrive. Often he finds himself swimming against the stream of the nation in which he finds himself.

Contrary to the state of the original Israelites, sometimes the laws of said nation to which they'd found themselves, ran counter to the Mosaic laws of God. This creates an even greater dilemma for the one who has commited himself to trusting Jesus. And God no longer had a literal nation to maintain, hence, the grace found in Jesus, of necessity, far exceeded that found in the tabernacle. He does atone for intentional sin as long as it is accompanied by genuine repentence.

One additional point which should be noted is that according to Hebrews, even Yom Kippur (Day of Atonement) only covers 'sins of ignorance':

'But only the high priest entered the inner room, and that only once a year, and never without blood, which he offered for himself and for the sins the people had committed in ignorance' (Heb 9:7, NIV)

It would indeed seem that Old Testament sacrifices did not cover anything beyond 'sins of ignorance'.