creating multiple variables/lists/functions via a loop (Maxima) - maxima

Question

below I have listed some ways to create variables/lists/functions via a for loop in Maxima,
but how, via a for loop, to do:
f1(x) := x^1$
f2(x) := x^2$
f3(x) := x^3$
example code:
for i : 1 thru 10 do
(x : concat ('a, i), x :: i)$
[a1, a2, a3, a4, a5, a6, a7, a8, a9, a10];
for i : 1 thru 3 do
(x : concat ('L, i), x :: [(3*i)-2,(3*i)-1,3*i])$
[L1, L2, L3];
/* good, but not quite what I want to do */
for i : 1 thru 3 do
f[i](x) := x^i$
[f[1](2), f[2](2), f[3](2)];
/* is there a way, via a for loop, to create */
f1(x) := x^1$
f2(x) := x^2$
f3(x) := x^3$
[f1(2), f2(2), f3(2)];
EDIT: further code:
/* is there a way, via a for loop, to create */
f(x) := x^1$
g(x) := x^2$
h(x) := x^3$
[f(2), g(2), h(2)];
for tmp1 : 1 thru 10 do
(tmp2 : parse_string(ascii(96+tmp1)), tmp2 :: tmp1)$
[a, b, c, d, e, f, g, h, i, j];
for tmp1 : 1 thru 10 do
(tmp2 : concat(parse_string(ascii(96+tmp1)), tmp1), tmp2 :: tmp1)$
[a1, b2, c3, d4, e5, f6, g7, h8, i9, j10];
EDIT 2: original problems solved (any code improvements/simplifications welcome):
for i : 1 thru 3 do
eval_string(concat("f", i, "(x) := x^", i))$
[f1(2), f2(2), f3(2)];
for i : 1 thru 3 do
eval_string(concat(ascii(96+5+i), "(x) := x^", i))$
[f(2), g(2), h(2)];
sum:0$
for i : 1 thru 3 do
sum:sum + eval_string(concat("f", i, "(2)"))$
sum;
sum:0$
for i : 1 thru 3 do
sum:sum + eval_string(concat(ascii(96+5+i), "(2)"))$
sum;

Answer 1

What is your larger goal here? In general using subscripted symbols e.g. a[1] instead of a1 is to be preferred. When you define a subscripted function, you only define it once, not for every value of the subscript. E.g.
(%i1) f[i](x) := x^i $
(%i2) [f[1], f[2], f[3]];
2 3
(%o2) [lambda([x], x), lambda([x], x ), lambda([x], x )]
(%i3) [f[1](u), f[2](v), f[3](w)];
2 3
(%o3) [u, v , w ]
If that doesn't work for you, maybe you can explain about what you're trying to achieve.

Answer 2

I have collected here, various ways of creating multiple variables/lists/functions via a loop in Maxima,
as an answer to the question, '[f1(2), f2(2), f3(2)]' explicitly answers the original question:
for i : 1 thru 10 do
(x : concat ('a, i), x :: i)$
[a1, a2, a3, a4, a5, a6, a7, a8, a9, a10];
for i : 1 thru 3 do
(x : concat ('L, i), x :: [(3*i)-2,(3*i)-1,3*i])$
[L1, L2, L3];
for tmp1 : 1 thru 10 do
(tmp2 : parse_string(ascii(96+tmp1)), tmp2 :: tmp1)$
[a, b, c, d, e, f, g, h, i, j];
for tmp1 : 1 thru 10 do
(tmp2 : concat(parse_string(ascii(96+tmp1)), tmp1), tmp2 :: tmp1)$
[a1, b2, c3, d4, e5, f6, g7, h8, i9, j10];
for i : 1 thru 3 do
eval_string(concat("f", i, "(x) := x^", i))$
[f1(2), f2(2), f3(2)];
for i : 1 thru 3 do
eval_string(concat(ascii(96+5+i), "(x) := x^", i))$
[f(2), g(2), h(2)];
f[i](x) := x^i$
[f[1], f[2], f[3]];
[f[1](2), f[2](2), f[3](2)];
[f[1](u), f[2](v), f[3](w)];