user471: After attaining Nibbana, did the Buddha still have intention (cetanā)?
In SN 12.2, intention is part of name in name-and-form. In SN 12.38 (quoted below), it sounds like intention is removed in an arahant.
For example, in the Udana 6.1 quote below, did the Buddha have the intention (cetanā) to go and sit at the Pavala shrine on a sitting cloth with Ananda for the day's abiding?
How does the Buddha's apparent intention in Udana 6.1, not conflict with the quote from SN 12.38?
From Udana 6.1:

I have heard that on one occasion the Blessed One was staying near
  Vesālī at the Gabled Hall in the Great Forest. Then, early in the
  morning, he adjusted his under robe and — carrying his bowl & robes —
  went into Vesālī for alms. Then, having gone for alms in Vesālī, after
  the meal, returning from his alms round, he addressed Ven. Ānanda,
  "Get a sitting cloth, Ānanda. We will go to the Pāvāla shrine for the
  day's abiding."
Responding, "As you say, lord," to the Blessed One, Ven. Ānanda
  followed along behind the Blessed One, carrying the sitting cloth.
  Then the Blessed One went to the Pāvāla shrine and, on arrival, sat
  down on the seat laid out.
Seated, the Blessed One addressed Ven. Ānanda, "Vesālī is refreshing,
  Ānanda. Refreshing, too, are the Udena shrine, the Gotamaka shrine,
  the Sattamba shrine, the ManySon shrine, the Sāranda shrine, the
  Pāvāla shrine.

From SN 12.38:

“Bhikkhus, what one intends, and what one plans and whatever one has
  a tendency towards (yañca ceteti yañca pakappeti yañca anuseti): this becomes a basis for the maintenance of
  consciousness. When there is a basis there is a support for the
  establishing of consciousness. When consciousness is established and
  has come to growth, there is the production of future renewed
  existence. When there is the production of future renewed existence,
  future birth, aging-and-death, sorrow, lamentation, pain, displeasure,
  and despair come to be. Such is the origin of this whole mass of
  suffering.


user43: Well yeah, that impulse to go to a certain place is an example of intention. However, intention to sit in meditation, is like intention of nothing, it is an intention of dispassion, of suchness. It is not an intention to get some object or attain some goal.
As that quote says, the intention shapes our mind to become what one intends, but if one intends on peace and suchness of meditation, what does one become?
Intention to meditate is not like other intentions, because the right meditation is dispassion, is letting go. This is why it is so hard for the worldly people to meditate. Because when you meditate you don't fuel your fire, not pursuing any goal, so it goes contrary to all our habits of being driven by our projects and impulses. 
So, intention that is inclined towards dispassion is not an "upadana" (fueling) intention. 

user14468: 
OP: After attaining Nibbana, did the Buddha still have intention (Cetanā)?

Yes, Lord Buddha still has intention (Cetanā) after attaining sopadhishesa-nibbana. But after attaining anupadhishesa-nibbana , everything including intention will be ceased without remainder.
Intention (Cetanā) is one of seven universal mental factors which can be seen in every consciousness. So, if there's consciousness present intention is also present. A sentient being (including Arahants) can think, speak, and do things using body because of this "cetanā" mental factor. Even-though it appears in resultant consciousness this mental factor is not manifested in those kinds of consciousness because of the weakness of its appearance with few other mental factors.

Cetana...is the mental factor that is concerned with the actualization of a goal, that is, the conative or volitional aspect of cognition. Thus it is rendered volition. The Commentaries explain that cetana organizes its associated mental factors in acting upon the object. Its characteristic is the state of willing, its function is to accumulate (kamma), and its manifestation is coordination. Its proximate cause is the associated states. Just as a chief pupil recites his own lesson and also makes the other pupils recite their own lessons, so when volition starts to work on its object, it sets the associated states to do their tasks as well. Volition is the most significant mental factor in generating kamma, since it is volition that determines the ethical quality of the action.

~ Cited form: Cetanā by Bhikku Bodhi
Intention (Cetanā) does not become kamma in every consciousness. Intention in resultant and functional consciousness don't become kamma. Intention in super-mundane consciousness can be also considered as not kamma because they ease the burden of aggregates and shorten the Samsara.

OP: For example, in the Udana 6.1 quote below, did the Buddha have the intention (Cetanā) to go and sit at the Pavala shrine on a sitting cloth with Ananda for the day's abiding?

Yes, you can understand this by the explanation I have provided above.

OP: How does the Buddha's apparent intention in Udana 6.1, not conflict with the quote from SN 12.38?

It's very hard for a worldling to imagine how Arahants think or what kind of thoughts they have. Let me explain this with an example. Suppose there are two people worship Lord Buddha at the same time. One is a worldling and the other is an Arahant. The action, "worship" can be led by the intention of "reappear in a heavenly sphere in the next existence" or "attaining Nibbana" for the worldling. But for Arahant the "intention" is none of the aforesaid. An Arahant has already done what should be done. It's hard to imagine what the intention of Arahant is.
But one thing can be assured. That is the intention of an Arahant is not associated with craving (Taṇhā), view (Diṭṭhi), and conceit (Māna).
Note: This is how I understood. I may be wrong but not Dhamma.

user471: I'm just adding this here for completeness, but I won't accept my own answer.

“Bhikkhus, what one intends, and what one plans, and whatever one has
  a tendency towards (yañca ceteti yañca pakappeti yañca anuseti): 
  this becomes a basis for the maintenance of consciousness."
“If, bhikkhus, one does not intend, and one does not plan, but one
  still has a tendency towards something, this becomes a basis for the
  maintenance of consciousness.

That is: what one intends AND what one plans AND whatever one has a tendency towards - so that means underlying tendencies (anusaya) are mandatory for the basis for the maintenance of consciousness.
So, the Buddha had intention and planning, without underlying tendencies.

user700: Arahants don't have karmic intentions and they don't seek any results. They have higher wisdom, higher goodness, higher intelligence that is not possible to measure or described by the ordinary way of thinking. The cause of their actions are not connected to any ordinary human intention, desire or mind state but it happens out of complete purity and wisdom of Nibbana. Even If an Arahant say that "It's my intention" or "It is not my intention" that's only words(which are just tools to communicate with humans) and words have limitations to explain things correctly. So obviously Buddha didn't have intentions but it is not possible to describe the root of an Arahant's actions because they attained Nibbana permanently and Nibbana is the formless state.
A part of this video(5:08-5:35) is about this subject:
https://youtu.be/GRquhvbfVp4?t=308

471: <p>After attaining Nibbana, did the Buddha still have intention (<em>cetanā</em>)?</p>

<p>In <a href="https://suttacentral.net/sn12.2/en/bodhi" rel="noreferrer">SN 12.2</a>, intention is part of name in name-and-form. In <a href="https://suttacentral.net/sn12.38/en/bodhi" rel="noreferrer">SN 12.38</a> (quoted below), it sounds like intention is removed in an arahant.</p>

<p>For example, in the Udana 6.1 quote below, did the Buddha have the intention (<em>cetanā</em>) to go and sit at the Pavala shrine on a sitting cloth with Ananda for the day's abiding?</p>

<p>How does the Buddha's apparent intention in Udana 6.1, not conflict with the quote from SN 12.38?</p>

<p>From <a href="https://www.accesstoinsight.org/tipitaka/kn/ud/ud.6.01.than.html" rel="noreferrer">Udana 6.1</a>:</p>

<blockquote>
  <p>I have heard that on one occasion the Blessed One was staying near
  Vesālī at the Gabled Hall in the Great Forest. Then, early in the
  morning, he adjusted his under robe and — carrying his bowl &amp; robes —
  went into Vesālī for alms. Then, having gone for alms in Vesālī, after
  the meal, returning from his alms round, he addressed Ven. Ānanda,
  <strong>"Get a sitting cloth, Ānanda. We will go to the Pāvāla shrine for the
  day's abiding."</strong></p>
  
  <p>Responding, "As you say, lord," to the Blessed One, Ven. Ānanda
  followed along behind the Blessed One, carrying the sitting cloth.
  Then the Blessed One went to the Pāvāla shrine and, on arrival, sat
  down on the seat laid out.</p>
  
  <p>Seated, the Blessed One addressed Ven. Ānanda, "Vesālī is refreshing,
  Ānanda. Refreshing, too, are the Udena shrine, the Gotamaka shrine,
  the Sattamba shrine, the ManySon shrine, the Sāranda shrine, the
  Pāvāla shrine.</p>
</blockquote>

<p>From <a href="https://suttacentral.net/sn12.38/en/bodhi" rel="noreferrer">SN 12.38</a>:</p>

<blockquote>
  <p>“Bhikkhus, <strong>what one intends, and what one plans and whatever one has
  a tendency towards (yañca ceteti yañca pakappeti yañca anuseti)</strong>: this <strong>becomes a basis for the maintenance of
  consciousness</strong>. When there is a basis there is a support for the
  establishing of consciousness. When consciousness is established and
  has come to growth, there is the production of future renewed
  existence. When there is the production of future renewed existence,
  future birth, aging-and-death, sorrow, lamentation, pain, displeasure,
  and despair come to be. Such is the origin of this whole mass of
  suffering.</p>
</blockquote>
 43: <p>Well yeah, that impulse to go to a certain place is an example of intention. However, intention to sit in meditation, is like intention of nothing, it is an intention of dispassion, of suchness. It is not an intention to get some object or attain some goal.</p>

<p>As that quote says, the intention shapes our mind to become what one intends, but if one intends on peace and suchness of meditation, what does one become?</p>

<p>Intention to meditate is not like other intentions, because the right meditation is dispassion, is letting go. This is why it is so hard for the worldly people to meditate. Because when you meditate you don't fuel your fire, not pursuing any goal, so it goes contrary to all our habits of being driven by our projects and impulses. </p>

<p>So, intention that is inclined towards dispassion is not an "upadana" (fueling) intention. </p>
 14468: <blockquote>
<p><strong>OP:</strong> After attaining Nibbana, did the Buddha still have intention (Cetanā)?</p>
</blockquote>
<p>Yes, Lord Buddha still has intention (Cetanā) after attaining sopadhishesa-nibbana. But after attaining anupadhishesa-nibbana , everything including intention will be ceased without remainder.</p>
<p>Intention (Cetanā) is one of seven universal mental factors which can be seen in every consciousness. So, if there's consciousness present intention is also present. A sentient being (including Arahants) can think, speak, and do things using body because of this &quot;cetanā&quot; mental factor. Even-though it appears in resultant consciousness this mental factor is not manifested in those kinds of consciousness because of the weakness of its appearance with few other mental factors.</p>
<blockquote>
<p>Cetana...is the mental factor that is concerned with the actualization of a goal, that is, the conative or volitional aspect of cognition. Thus it is rendered volition. The Commentaries explain that cetana organizes its associated mental factors in acting upon the object. Its characteristic is the state of willing, its function is to accumulate (kamma), and its manifestation is coordination. Its proximate cause is the associated states. Just as a chief pupil recites his own lesson and also makes the other pupils recite their own lessons, so when volition starts to work on its object, it sets the associated states to do their tasks as well. Volition is the most significant mental factor in generating kamma, since it is volition that determines the ethical quality of the action.</p>
</blockquote>
<p>~ Cited form: <a href="https://en.wikipedia.org/wiki/Cetan%C4%81#Theravada" rel="nofollow noreferrer">Cetanā</a> by Bhikku Bodhi</p>
<p>Intention (Cetanā) does not become kamma in every consciousness. Intention in resultant and functional consciousness don't become kamma. Intention in super-mundane consciousness can be also considered as not kamma because they ease the burden of aggregates and shorten the Samsara.</p>
<blockquote>
<p><strong>OP:</strong> For example, in the Udana 6.1 quote below, did the Buddha have the intention (Cetanā) to go and sit at the Pavala shrine on a sitting cloth with Ananda for the day's abiding?</p>
</blockquote>
<p>Yes, you can understand this by the explanation I have provided above.</p>
<blockquote>
<p><strong>OP:</strong> How does the Buddha's apparent intention in Udana 6.1, not conflict with the quote from SN 12.38?</p>
</blockquote>
<p>It's very hard for a worldling to imagine how Arahants think or what kind of thoughts they have. Let me explain this with an example. Suppose there are two people worship Lord Buddha at the same time. One is a worldling and the other is an Arahant. The action, &quot;worship&quot; can be led by the intention of &quot;reappear in a heavenly sphere in the next existence&quot; or &quot;attaining Nibbana&quot; for the worldling. But for Arahant the &quot;intention&quot; is none of the aforesaid. An Arahant has already done what should be done. It's hard to imagine what the intention of Arahant is.</p>
<p>But one thing can be assured. That is the intention of an Arahant is not associated with craving (Taṇhā), view (Diṭṭhi), and conceit (Māna).</p>
<p><em>Note: This is how I understood. I may be wrong but not Dhamma.</em></p>
 471: <p>I'm just adding this here for completeness, but I won't accept my own answer.</p>

<blockquote>
  <p>“Bhikkhus, what one intends, and what one plans, and whatever one has
  a tendency towards <strong>(<em>yañca ceteti yañca pakappeti yañca anuseti</em>)</strong>: 
  this becomes a basis for the maintenance of consciousness."</p>
  
  <p>“If, bhikkhus, one does not intend, and one does not plan, but one
  still has a tendency towards something, this becomes a basis for the
  maintenance of consciousness.</p>
</blockquote>

<p>That is: what one intends AND what one plans AND whatever one has a tendency towards - so that means <a href="https://suttacentral.net/an7.11/en/sujato" rel="nofollow noreferrer">underlying tendencies (<em>anusaya</em>)</a> are mandatory for the basis for the maintenance of consciousness.</p>

<p>So, the Buddha had intention and planning, without underlying tendencies.</p>
 700: <p>Arahants don't have karmic intentions and they don't seek any results. They have higher wisdom, higher goodness, higher intelligence that is not possible to measure or described by the ordinary way of thinking. The cause of their actions are not connected to any ordinary human intention, desire or mind state but it happens out of complete purity and wisdom of Nibbana. Even If an Arahant say that "It's my intention" or "It is not my intention" that's only words(which are just tools to communicate with humans) and words have limitations to explain things correctly. So obviously Buddha didn't have intentions but it is not possible to describe the root of an Arahant's actions because they attained Nibbana permanently and Nibbana is the formless state.</p>

<p>A part of this video(5:08-5:35) is about this subject:</p>

<p><a href="https://youtu.be/GRquhvbfVp4?t=308" rel="nofollow noreferrer">https://youtu.be/GRquhvbfVp4?t=308</a></p>
