How do I INSERT the output from an SQL COUNT statement into a table?

Just possibly this query more rightly belongs on a MySQL forum, but rather than going to all the trouble necessary for me to join yet another support site, I thought I might post a query here.
Besides, it arises from my attempt to upgrade a very old version of Drupal (4.x I think). I am trying to see what tables are updated when I update the content of a Drupal 6.x web-site in various ways -- adding a node, adding a comment, adding a tag, changing the menu, etc. This will help me to understand how to import my older web-site into Drupal version 6.x .
So I need to count the rows in each table before and after the change. Where the row counts differ, that table has been updated.
To store the data, I create another table, rowcount:
drop table rowcount;create table rowcount(tname varchar(64), f1name varchar(64), rcount integer);
... Then, for each table, I find out the row count for each table and store it together with the table name and and the name of a field or column[1] in the table:
INSERT INTO rowcount (tname, f1name, rcount) VALUES ("access", "aid", select COUNT(*) from `access`);
The above SQL statement does not work, even though the SQL statement contained in the above INSERT statement:
select COUNT(*) from `access`
... does work. The error I get is the following:
ERROR 1064 (42000): You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'select COUNT(aid) from `access`)' at line 1
How is it possible to INSERT the value obtained by the COUNT function using the same SQL statement?
If it is not possible to do this with one SQL statement, how should I go about it?
(I have already searched and searched all over the web and found nothing that works with MySQL.)
Footnotes
[1] COUNT apparently needs a field name to work. I arbitrarily chose to use the name of the first field in each table. In the above example, 'aid' is the name of the first field in the table.