It should not bend at all without crimping. That you should be able to
hold a five foot section horizontal and not have it bend or sag. It should
be smooth inside and out. That sounds like what you have.

Yes the vertical part is smooth inside and out, but the cross section is
not purely circular or rectangular. Instead, it is like an eclipse:

---------
///- -\\\
// \\
/ \
|| ||
| |
| |
| |
| |
| |
|| ||
-----------------------
\-------------------/


The solid stuff is crimped on one end and that crimped end slips inside
the end of the last pipe. In a dryer vent the crimp ends should always be
at the end away from the dryer. In some applications screws are used to
secure them, but for a dryer the screws will cause lint build up and they
should only be taped using real "duct" tape not duck tape. The other stuff is often attached using some sort of clamp.

I still do not understand how the the vertical part connects to the
horizontal part. Since the horizontal part is of large caliber, how can
the vertical part seamlessly connects to it? I can think of two cases,
as shown in the two figures below). Which case is more like the reality?
And, did I break that connection (see my original post)?

CASE 1:

+---------------------------------------------+
|---------------------------------------------|
+------+----+---------------------------------------------|
|IIIIIIIIIIIIIIII|----------------------------------------|
|IIIIIIIIIIIIIIII|----------horizontal-pipe---------------|
+IIIIIII----+---------------------------------------------|
|IIIIII| |---------------------------------------------|
|IIIIII| +---------------------------------------------+
|IIIIII| out
|IIvIII| of
|IIeIII| the
|IIrIII| house
|IItIII|
|IIIIII|
+-----+IIIIII+
|IIIIIIIIIIII|
|IIIIIIIIIIII|
+-----+------+
To Dryer

CASE 2:


*----------------------------------------+
/-----------------------------------------|
/------------------------------------------|
*II*----------------------------------------|
|III\---------------------------------------|
|IIII\--------------------------------------|
|IIIII\+------------------------------------+
|IIIIII|
|IIIIII|
|IIIIII|
|IIIIII|
|IIIIII|
|IIIIII|
|IIIIII|
|IIIIII|
+IIIII+IIIIII+
|IIIIIIIIIIII|
|IIIIIIIIIIII|
+-----+------+

To Dryer