Since the result is clearly a real number I presume you seek an algebraic computation on real values only:

(64*abs(b)^4+4*(a-2)*((a-2)*abs(sinh(c))^2-8*Im(b)*Re(sinh(c))+8*Re(b)*Im(sinh(c)))*abs(b)^2+a^2*(16*Im(b)^2-4*Im(b)*(a-2)*Re(sinh(c))-16*Re(b)^2-4*Re(b)*(a-2)*Im(sinh(c))+a^2))/(4*abs(b)^2*abs(sinh(c))^2+a*(-4*Im(b)*Re(sinh(c))-4*Re(b)*Im(sinh(c))+a));

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If you are trying to view text form of your formula then lprint it.
lprint(expand(Q(h)));

Can you verify this formula?
 

((product(q^i - 1, i = n + 1 - r .. n - 1))^2*((-(q^n - q - 1)^2 + q + 1)/(q^r)
   + ((q^n - 1)^2*(q^n - q)^2)/((q^r - 1)*(q^n)^2) - ((q^n)^2)/((q^r)^2))*
  q^(1/2*r^2)*q^(- 1/2*r)*(q^n)^2)/((product(q^i - 1, i = 1 .. r - 1))*q^2);

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I think your second code is equivalent to the following;
evalf(''Pi'');
eval(evalf(''Pi''));
evalf(eval(evalf(''Pi'')));

It should have been:
evalf(''Pi''):
evalf('"');

If you want to use solve in your example then you can simply use this option:
[solve]({0 < 272*c^3-213*c^2+52*c-4}, c, real, explicit = false); evalf(%); evalc(convert(%%, radical));

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Is this form more acceptable:

Your expression is always a root (in lambda) of one of these:

3*lambda^2+(l^4+36)*lambda+3*l^4+108
-3*lambda^4+((3/2)*l^4+18)*lambda^3+(l^8+(141/4)*l^4+81)*lambda^2+(3/2)*(l^4-12)*(l^4+18)*lambda+81*l^4-972
162+2*lambda^4+(l^4+24)*lambda^3+((7/2)*l^4+108)*lambda^2+(3*l^4+216)*lambda
l^4*lambda+3*l^4-3*lambda^2

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How about this:

sys := {w = -2*Pi*i*k_2*v + 2*Pi*i*k_2*(4*K^2)/(5*Pi)*u, z = -2*Pi*i*k_1*v + 2*Pi*i*k_1*(4*K^2)/(5*Pi)*u, p*s*x = -2*Pi*i*k_1*u - 4*Pi^2*(k_1^2 + k_2^2)*x + a_1, p*s*y = -2*Pi*i*k_2*u - 4*Pi^2*(k_1^2 + k_2^2)*y + a_2, k_1*z + k_2*w = 0, k_1*x + k_2*y = 0};
sys union {-RootOf(_Z^2+1)*z-w, RootOf(_Z^2+1)*x+y};
solve(% union {w<>0});
map2(remove, evalb, [%]);
eliminate(%[1], {x, y, z, u, v, w});
collect(%, [Pi, K], factor);

In the title.
                                 

First look at this:

(() -> solve({args}, indets({args}, name) minus {t}))(eq || (`$`(1 .. 4)));
subs(t = 0, %);
allvalues(%);

Clearly your equations are incomplete.

Could it be that you need a registered version of Maple?

How about:
plot(floor(x/3)*3, x=-5..5);
 

Simply compare these two codes:

restart;
P1 := 1007;
P2 := 1014;
P3 := 1014.1;
evalf(P2 - P1, 2);
evalf(P3 - P1, 2);

restart;
P1 := 1007.;
P2 := 1014.;
P3 := 1014.1;
evalf(P2 - P1, 2);
evalf(P3 - P1, 2);

The difference is obvious. No bugs here.

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For Your matrix you can use this:

F := (n, f) -> LinearAlgebra:-BandMatrix(map(f, [$1 .. n]), 0, n);
F(4, (n) -> d[n]);

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for i from 1 to n do proc(i, a, b) a[i]:=b[i] end(i, a ,b) od;

also

for i from 1 to n do proc(i) a[i]:=b[i] end(i) od;

provided a, b are not declared local.