@Adam Ledger  See the help page  remember (Option remember in Procedures)  for this.

@tiaranain  Change the last line to
plots:-fieldplot3d( RHS, x=-1..1, y=-1..1, z=-1..1, arrows=THICK, color=red,  grid=[5,5,5], axes=box);
 

@Zeineb  because 180 is divided by 90 without a remainder. Strictly speaking, only one second case can be left, because 0 is also divisible by 90.

@tiaranain  I fixed your syntax errors below:

SYS := [D(x)(t)=x(t)-x(t)*y(t)-x(t)*z(t),
D(y)(t)=-0.4*y(t)+x(t)*y(t),
D(z)(t)=-0.24*z(t)+x(t)*z(t)];

RHS := eval( map( rhs, SYS ), [x(t)=x,y(t)=y,z(t)=z] );
                             
plots:-fieldplot3d( RHS, x=-1..1, y=-1..1, z=-1..1, grid=[5,5,5], axes=boxed );

@Earl 

LongSum:=proc(f,n0,n)
uses InertForm;
Display(`%+`(seq(f(k),k=1..n0))+`...`+f(n));
end proc:

Examples:
LongSum(n->x[n], 2, n);
LongSum(n->n/(n+1), 3, k);
LongSum(n->n/(n+1), 3, 100);

@minhthien2016  The code shows that this property is also true for a non-convex quadrilateral (in this example). If you still need a convex one, take the point symmetric to DD with respect to the AC. Then you get a convex quadrilateral with the same side lengths.

@tomleslie 
 

isEquiv(Pi*x+y=Pi, x+y/Pi=1); 
isEquiv(x-I*y=I, I*x+y=-1);
isEquiv(sin(x)^2+cos(x)^2=1, 1=1);

Here is my version, which works for these examples:

g:= z-> simplify( (lhs(z)-rhs(z))):
isEquiv1:= (x,y)-> is(simplify(g(x)-g(y))=0 or type(simplify(evalc(g(x)/g(y))),complexcons)):

@Christian Wolinski 

'cos'(Pi/2-op(1,convert((1/2)*sqrt(3)*sin(y)+(1/2)*cos(y), phaseamp, y)));

@Caneee315 A parallelogram rule is used to add two vectors. See an example below. The animation in this example can be done analogously to the example above:

restart;
with(plots):	
u, v:=[1, 2, 3], [-1, 2, 3]:
U:=arrow(u, color=blue, width=0.1):
V:=arrow(v, color=blue, width=0.1):
W:=arrow(u+v, color=red, width=0.1):
L1:=plottools:-line(u,u+v, linestyle=2, thickness=3, color=black):
L2:=plottools:-line(v,u+v, linestyle=2, thickness=3, color=black):
display(U,V,L1,L2,W, axes=normal, orientation=[-115,15,120]);

@Jayaprakash J  Your function depends on 2 variables  x  and  alpha . Therefore, if you want to build it as a function of alpha, then you need to fix the value of  x . Or plot the function of two variables using the plot3d command:

f:=x->-0.3075000000e-1*x^2-0.2145927617e-3*x^6-0.2692226562e-4*x^4+0.3750551906e-2*x^5+0.1050625000e-2*x^3-0.5266789021e-5*x^7+0.1082238239e-4*x^9-6.80130209*10^(-7)*x^6*sin(alpha)+0.2932994791e-5*x^6*cos(alpha)+0.4375000000e-2*x^4*cos(alpha)-0.7990625000e-4*x^5*sin(alpha)-0.1704062500e-3*x^5*cos(alpha)-3.907366066*10^(-7)*x^8*cos(alpha)^2-0.5000000000e-1*x^3*sin(alpha)+0.3375000000e-2*x^4*sin(alpha)-0.2231049199e-3*x^7*sin(alpha)+0.1723809524e-4*x^7*cos(alpha)^2-0.5000000000e-1*x^3*cos(alpha)+7.912017277*10^(-7)*x^8+0.4464285714e-3*x^7*cos(alpha)^3-0.6695959034e-3*x^7*cos(alpha)+0.4337937076e-4*x^9*cos(alpha)^2-0.982142856e-5*x^8*cos(alpha)^3+0.3392338088e-4*x^8*cos(alpha)+0.4906693567e-5*x^8*sin(alpha)+0.4412678315e-5*x^9*cos(alpha)+0.1833880452e-5*x^9*sin(alpha)+6.885206662*10^(-7)*x^10-0.1833333334e-3*x^6*cos(alpha)^2+.6*x+1:
G:=D(f)(x);
plot(eval(G, x=1), alpha=-Pi..Pi);
plot3d(G, alpha=-Pi..Pi, x=0..1);

@Carl Love  Yes of course.

The record  12^6^5   is ambiguous. It can be understood as  (12^6)^5  or as  12^(6^5) .

@Carl Love  To prevent extra zeros in output  , we can solve symbolically using the simplex:-maximize  command:

simplex:-maximize(P.V, {seq(C.V <=~ R), seq(V >=~ 0)});
eval(P.V, %);
                          {F = 50, K = 150}
                                 8500
 

@Jayaprakash J  In Maple 2018.2, the code works correctly. You probably have an earlier version of Maple. Try the following option:

restart;
f:=1+B*x-(1/12)*B*x^3+0.1666666667e-4*B^3*x^3-4.166666667*10^(-8)*B^4*x^4+(1/160)*B*x^5+8.333333333*10^(-11)*B^5*x^5-0.5000000000e-2*B^2*x^2+0.1666666667e-4*B*x^3*C^2-4.166666667*10^(-8)*B*x^4*C^3+8.333333333*10^(-11)*B*x^5*C^4-0.5000000000e-2*B*C*x^2+0.3333333333e-4*B^2*x^3*C-1.250000000*10^(-7)*B^3*x^4*C-1.250000000*10^(-7)*B^2*x^4*C^2+3.333333333*10^(-10)*B^4*x^5*C+5.000000000*10^(-10)*B^3*x^5*C^2+3.333333333*10^(-10)*B^2*x^5*C^3+0.7291666667e-3*B*x^4*C-0.3333333333e-5*B*x^5*C^2+0.6250000000e-3*B^2*x^4-0.2083333333e-5*B^3*x^5-0.5416666667e-5*B^2*x^5*C:
Explore(plot(f, x=-4..4, view=-10..10), parameters=[B=-5...5., C=-5...5.]);

@vv  I use Maple 2018.2  64 bit