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Worship ( العبادة) is defined as:

A comprehensive term that incorporates everything that Allaah loves and is pleased with from the statements and actions, both inward and outward.

And thus, worship is of many different types, and they are mentioned in the Qur'an. And when something is declared to be worship, then it is not permissible for it to be directed to other than Allaah, and such worship occurs either in the heart, upon the tongue or through the limbs, all the forms and types of worship fall into any of these three categories.

Du'a (invocation) is worship
From its proofs are the saying of Allaah:

 So, call you (O Muhammad and the believers) upon (or invoke) Allah, making (your) worship pure for Him (Alone)... (Ghafir 40:14) 

Ibn Katheer commented:

Meaning, make your worship and your invocation purely and sincerely for Allaah alone, and oppose the pagans in their way and their religion.

And the pagans invoke others besides Allaah, hoping for their intercession or seeking them as a means of approach to Allaah, and Allaah refuted this in the Qur'an, and ordered that only He be invoked.
And also the saying of Allaah:

 Invoke your Lord with humility and in secret... (Al-A'raf 7:55) 

And also the saying of Allaah:

 And the mosques are for Allah (Alone), so invoke not anyone along with Allah. (Al-Jinn 72:18) 

Ibn Katheer comments:

The Most High says, commanding His slaves that they single Him out in arena of His worship and that none is invoked alongside Him...

And Ibn Jareer at-Tabari comments:

...[meaning], and do not associate anyone as a partner to Him therein, but rather single Him out with Tawhid (Pure Monotheism) and make worship purely and sincerely for Him (alone)...

And also the saying of Allaah:

 So invoke not with Allah another ilah (god, deity) lest you be among those who receive punishment. (Ash-Shu'ara 26:213) 

And also the saying of Allaah:

 And who is more astray than one who calls (invokes) besides Allýh, such as will not answer him till the Day of Resurrection, and who are (even) unaware of their calls (invocations) to them? And when mankind are gathered (on the Day of Resurrection), they (false deities) will become enemies for them and will deny their worshipping. (Al-Ahqaf 46:6) 

And there are many similar verses in this regard, through which it is firmly established that du'a (invocation) is worship and thus is not to be directed except to Allaah alone.
Calling Upon Someone In A Matter In Which They Have Ability
All of the above verses are in reference to supplication (du'a) in such matters that only Allaah alone has the power over and thus whoever invoked others besides Allaah for that in which only Allaah has power over, then he has committed shirk (associationism) and kufr (disbelief), irrespective of whether the one being called upon is living or dead.
As for invoking a living person for that in which he is capable, such as saying, "O so and so, feed me", or saying, "O so and so, give me drink", or saying, "O so and so, help me to carry these goods" and so on, then there is no harm in this.
And whoever called upon one who is dead, or who is absent (i.e. not present there and then) with the likes of these requests (food, drink, assistance and so on), then he has committed shirk (associationism), because the dead and the absent are not able to provide the likes of these affairs, and a person would not have called upon them for these things except due to his belief that they are able to provide these things whilst being absent, and if he had not believed this, he would not have called upon them, rather he would have called upon Allaah alone.

Du'a Is Of Two Types: That Of Need and That of worship
The Scholars explain that du'a is of two types, the first is an explicit request made such as "O Allaah, forgive me!", and "O Allaah provide for me!" and "O Allaah, show mercy to me!" and "O Allaah guide me!" and "O Allaah, grant me a righteous spouse", and "O Allaah grant me success!" and so on. All of these are specific requests, for specific needs and this is called (دعاء المسألة), "The invocation of need". This type of du'a is accompanied with other forms of worship, particularly those of the heart, such as love, hope, aspiration, reliance, awe and the likes.
As the for second, (دعاء العبـادة), "the invocation of worship", then this covers every act of worship in the sense that when you perform any act of worship, whether it is inward, outward, verbal or non-verbal, then even if you are not expressing it explicitly with your tongue, you are nevertheless, by way of the performance of that action, asking from Allaah. For example, by giving charity, which is worship, you are asking, by way of your action, even if you do not verbally express it, for reward, mercy and forgiveness and the likes. And the same applies to all other actions of worship. Thus, this is called "the invocation of worship", in the sense that you are invoking Allaah (silently) through the actions you are performing.
Now both of these two types of worship are intended by the verses that are mentioned above, and when you refer back to the classical commentaries of the Qur'an you find that they use du'a, interchangeably with ibaadah, because that is exactly how it has been used in the Qur'an.

Prohibition of Invoking Others Besides Allaah
From the above, everything that occurs in the Qur'an of the command to invoke Allah and Him alone, praising of those who invoke only Him alone, the prohibition of invoking others, and the absence of any benefit of invoking others besides Allaah, as occurs frequently in the Qur'an, then this applies to both forms of invocationmentioned above.
The issue of invocation is also connected to other forms of worship such asisti'aanah (seeking aid), isti'aadah (seeking refuge) and istighaathah (seeking rescue), and these will be dealt with separately in other articles.