The intellect is the tool given to Man to understand and distinguish between right and wrong, good and evil, and the reason why there are different levels of perfection.
Yet even this magnificent being we call the intellect, has its limits in knowledge of the Divine, to the extent that it is unable to identify the interests of mankind in this world, much less the hereafter and its laws.
Therefore it needs an external aid, in the form of revelation from God to His noble Messengers and Prophets.
Hence, the relationship between religion and intellect becomes clear, where religion plays the role of guidance on the straight path to perfection, and the intellect the role of the lantern that illuminates this road. This relationship is such that one cannot exist without the other. Without an intellect, one would not be able to identify the correct road that would lead to the desired goal, in the same instant, a person could have an intellect, yet if the correct path is no available to him, he would not be able to create one for himself.
رُسُلًا مُبَشِّرِينَ وَمُنْذِرِينَ لِئَلَّا يَكُونَ لِلنَّاسِ عَلَى اللَّهِ حُجَّةٌ بَعْدَ الرُّسُلِ ۚ وَكَانَ اللَّهُ عَزِيزًا حَكِيمًا
Messengers of good news and of warning, in order that mankind might have no argument against Allah after the messengers. Allah was ever Mighty, Wise. 
This verse indicates that there would have been no need for Messengers if our intellects had the sufficient knowledge capacity to avoid corruption and wrong-doing. Similar verses are numerous, and detailed explanation of which will come when I will post the proofs of the necessity for Prophethood:
مَّنِ اهْتَدَىٰ فَإِنَّمَا يَهْتَدِي لِنَفْسِهِ ۖ وَمَن ضَلَّ فَإِنَّمَا يَضِلُّ عَلَيْهَا ۚ وَلَا تَزِرُ وَازِرَةٌ وِزْرَ أُخْرَىٰ ۗ وَمَا كُنَّا مُعَذِّبِينَ حَتَّىٰ نَبْعَثَ رَسُولًا
Who receiveth guidance, receiveth it for his own benefit: who goeth astray doth so to his own loss: No bearer of burdens can bear the burden of another: nor would We visit with Our Wrath until We had sent an messenger (to give warning)
وَلَوْ أَنَّا أَهْلَكْنَاهُم بِعَذَابٍ مِّن قَبْلِهِ لَقَالُوا رَبَّنَا لَوْلَا أَرْسَلْتَ إِلَيْنَا رَسُولًا فَنَتَّبِعَ آيَاتِكَ مِن قَبْلِ أَن نَّذِلَّ وَنَخْزَىٰ
And if we had destroyed them with some punishment before it, they would assuredly have said: Our Lord! If only Thou hadst sent unto us a messenger, so that we might have followed Thy revelations before we were (thus) humbled and disgraced!
وَيَقُولُ الَّذِينَ كَفَرُوا لَوْلَا أُنزِلَ عَلَيْهِ آيَةٌ مِّن رَّبِّهِ ۗ إِنَّمَا أَنتَ مُنذِرٌ ۖ وَلِكُلِّ قَوْمٍ هَادٍ
Those who disbelieve say: If only some portent were sent down upon him from his Lord! Thou art a warner only, and for every folk a guide.