AQL

The word closest to the word AQL-عقل is Intellect/Reason in English.

Hadith:

Imam Ja'far Sadiq asked Imam Abu Hanifah: "Who is an intelligent man?

Imam Abu Hanifah: "One who can distinguish between good and bad".

Imam Ja'far: "An animal is also able to distinguish between good and bad. An animal recognizes a man who is kind and cruel to it."

Imam Abu Hanifah: "Who then is an intelligent person?"

Imam Ja'far: "A person who is able to distinguish between two good things and two evils, so that he may choose the better of the two good things and that he may be able to repel the worse of two evils."

(The rule of choosing the lesser evil applies when confronted by two evils and there is no third option. To save oneself from either of the evils has to be chosen. In such an eventuality, the lesser evil is adopted.)

Since Islam is the path that leads you to know Allah, starting from submitting and continuing on with this endless journey of knowing Allah, an Intelligent person from Islamic point of view, is a person who accepts Islam to embark on this amazing journey,according to the capacity, openness and sincerity, to receive the amazing gift of knowing Allah from Allah himself.

Hadith:

H 3, Ch. 1, h 3 - Al-Kafi

Imam Sadiq was asked: "What is Intelligence?" He replied, ‘It is a means thru which one worships Allah, the Merciful, and attains paradise.’ I then asked, "What was the thing with Mu’awiyah?" ‘It was shrewdness. Mischief is similar to Intelligence but it is not Intelligence.’ The Imam replied.

H 6, Ch. 1, h 6 - Al-Kafi

Ahmad ibn Idris has narrated from Muhammad ibn Hassa’n from abu Muhammad al-Razi from Sayf ibn ‘Umayra from Ishaq ibn ‘Ammar from abu ‘Abdallah (a.s) who has said the following.

" One who has Intelligence, has religion, and one who has religion, he enters Paradise."

And The Religion which is a Life style of full Submission to the Creator, is no other then:

Quran Aya:

إِنَّ الدِّينَ عِندَ اللَّهِ الْإِسْلَامُ ۗ

Religion with God is Islam (3:19)

The prophet reached the highest level of intelligence amongst the human beings, thru his deep desire to know the truth as it is and managed to stay pure,trust worthy,and humble, despite living amonsgt the most ignorant and unhumane people of his time.

Hence AQL( intelligence ) is a divine gift given to those who submit to the one God fully.

The conditions of receiving more of this divine gift is by:

1.Respecting and obeying the rules and guidlines given by The God Almighty for us to follow.

2.Pondering and thinking about Allah, his creations and having a healthy and respectful ,reflective and questioning mind in order to understand.

3.To be open to receive the truth, from the sources Allah has prescribed, at at all times, even though it may contradict our own perspective of observing and understanding.

Everything apart from the creator is a creation, hence even AQL/ intellect is a creation (creature) in Islamic teachings.

Al-Kafi the most prominent Shia hadith book,narrated by the Infallibles,starts with the Chapter of عقل-AQL (Intellect) and جهل-JAHL (Ignorance)

More Hadiths in Regards to Importance of AQL:

H 12, Ch. 1, h 12  Al-Kafi

"O Hisham, for everything there is a guide. ***The guide for intelligence is thinking. The guide for thinking is silence. For everything there is a means for mobility the means of mobility for intelligence is humble attitude. To disobey a prohibition is enough proof of ones ignorance.

"O Hisham, the commander of the true believers, Imam Ali (a.s) has said, "***Allah is worshipped better by no means other than intelligence. No one’s intelligence reaches perfection until therewith is found various qualities. 

1.Disbelief and evil should not emerge therefrom. 

2.Wisdom and goodness should be expected to exist therewith. 

3.The extra of the property of a person of intelligence is given in charity, 

4.the extra of his words is restrained and his share of the worldly things is only the basic necessities.

5.He never considers himself as to have learned enough.

6.To be with Allah, although in a very humble state, is far better to him than to live very much honored with others.

7. Humbleness is more beloved to him than being taken as a dignitary.

8. He considers virtuous deeds of others a great deal and his own virtuous deeds as insignificant.

9. He considers all the other people better than his self and his own self as the worse of all and this is the totality of all things."

H 19, Ch. 1, h 19  Al-Kafi

Ali ibn Ibrahim has narrated from his father from Yahya ibn al-Mubarak from ‘Abdallah ibn Jubla from ibn Ishaq ibn ‘Ammar from abu ‘Abdallah (a.s) who has said the following.

"I asked Imam abu ‘Abdallah (a.s) this, ‘May Allah take my soul in service for your cause, I have a neighbor who prays a great deal, gives much charity and very often visits Makka and he seems alright.’" The Imam (a.s) asked, "O ibn Ishaq ***how is his intelligence?" I then said, "May Allah take my soul in service for your cause, he does not have any intelligence" "Nothing from what he does will be raised up (to heavens)." Replied the Imam.

H 28, Ch. 1, h 28  Al-Kafi

A number of our people has narrated from Ahmad ibn Muhammad from certain persons of our people in a marfu‘ manner from abu ‘Abdallah (a.s) who has said the following.

"The Holy Prophet (s.a) has said, ‘***When you find a man who prays and fasts a great deal do not become proud of him until you see how his intelligence is." 

*Highly recommended Read: Al- Kafi

***Below is an Attached PDF from Al- Kafi refering to the list of qualities under Intelligence.