Day, Month & Year Drop Downs in Writer Doc - No Drop Arrows

Is there a preset Day/Month/Year drop down already made in ‘Writer’? This would save me some time.

As well, can I have this drop down without the drop down arrow in the box? Or, once the choice is selected, the arrow disappears? Either will suffice.

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Please, edit your question to elaborate more. The image you show doesn’t look like something you can achieve in Writer unless you designed a form. Are you using Calc?

Instead of hinting at some particular solution, describe your goal, this could make easier to point you on the right track.

I did a search for calendar on LO Extensions and templates site and found a couple of add-in calendars for Calc but none for Writer.

I installed one at random, calCalc, created a spreadsheet in Calc and copied and pasted special as LibreOffice 7.2 Spreadsheet into Writer. By double-clicking on the OLE table it opens the Calc functionality so I can open a calendar picker by Ctrl+right-click. As there is no list, there is no arrow. You can use Calc functionality too, e.g. Ctrl+; for today’s date. But there is only the date, not individual cells as shown in your image.

You may consider using a date control.
t72681.odt (9.4 KB)

Great suggestion!! Your suggestion made me find the ‘Date Field’ under ‘Form Control’. Thanks!!
1 question though, the date I have shown in the 'Standard (long). I would like the version of the date I posted but no ‘Day’ in the date. Is there an add-on feature to have the long date without the day of the week?
Any chance there is the option for no black arrow?

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Yes, the format options are limited. For “unlimited” formatting you can use a formatted field which is about the same as a spreadsheet cell.
I have chosen a date control with numeric format because the long dates with month names lack an important feature. You can place the text cursor at any of the 3 numbers and using the key-up/down arrows you can scroll through the time units day, month and year. The same works with the mouse wheel if you want that, unfortunately not with the textual dates.
You may turn off the drop down button which removes the drop down calendar.

Within LibreOffice Writer I have the calendar drop down as shown:
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When I export my form to PDF, I use ‘Export Directly as PDF’

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When I open that PDF, the calendar is no longer functional. The box is there but no drop down calendar:
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Clicking inside the box shows it as a text box:

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Am I doing something wrong?

The details depend on the PDF standard, how your PDF viewer implements the standard and if LibreOffice is able to translate every possible detail into that standard.
Do PDF forms exist that support the edit modes and drop-down calendars? I don’t know.