An auxiliary verb is a combination of Primary auxiliary and the modals.
An Auxiliary verb is a helping verb used with a main verb to form a verb phrase. It indicates tense, mood, grammatical aspects of the main verb.
Three primary forms of primary auxiliary verbs are : "Be", "Have", "Do"
1. Yes, I have a pen.
2. I am speaking to you now.
3. No. I did not do that.
Modals are also known as modal auxiliary verb. Modal Verbs are verbs that help the main verb to express one of the following:

The modal verbs are: Shall, Should, Will, Would, Can, Could, May, Might.
1. Shall I help you today?
2. You should always brush your teeth before going to bed.
3. Will you complete your homework on time?
4. Would you mind passing the plate?
5. Can you show me the way?
6. You could use the restroom on the right lobby instead.
7. May I know your name, please?
8. I might come for the exhibition tomorrow.
Some of the Primary auxiliary sentence from the lesson "Seventeen oranges" are:
1. I had read a lot of detective stories to make the mistake of blabbing.
2. Pongo and the other policeman had seen some carts at the dock gate.
3. Finally, Pongo understood what had happened.
4. You have to swallow all the evidence.
5. Have you anything to say?’
6. What will my father do?
Some of the Modals sentence from the lesson "Seventeen oranges" are:
1. Then Pongo looked at the table, and at first, he could not figure out what had happened.
2. The cat will run away.
3. ‘I can smell them,’ said the other policeman.
4. ‘But the cat will run away,’ Clem said again.
5. What will my father say?
6. I must swallow all the oranges, I thought. Only three left!