@Joe Riel The name is unintentionally inappropriate. I should've named it HasNegative.

@micahdavid That's not the same thing. Maple can do (numerically) the same integral that you passed to WolframAlpha:

int(1/Li(x), x= 2..2.1);

Li(x) for x > 1 is defined as the Cauchy Principal Value of Int(1/ln(t), t= 0..x). The integral starts at 0, not 2. Your inner integral starts at 2. Your integral is int(1/int(1/ln(x[1]), x[1]= 2..x[2]), x[2]= 2..2.1). It definitely diverges at its left endpoint. Since the divergence is at an endpoint, it cannot be saved by using Cauchy Principal Value.

@k20057 5 You can only use two equations, not three.

@k20057 5 There are only two parameters, and hence only two equations.

f:= E-> exp(-E/kT)/A:
eq1:= f(0) = ...:
eq2:= f(1) = ...:
....

@k20057 5 The system of equations cannot be solved with independent solutions for A and B because B/A is essentially a single coefficient.

What version of Maple are you using? Maple 18 accepts your code, and the unapply changes x[2] to x_2, which shouldn't make any difference because it is a dummy variable.

The equations are missing from your Question. Try including them in plain text form, or try attaching a worksheet.

The worksheet attachment of your post is missing. Please try uploading and attaching again.

What exactly is in the Excel worksheet? Is it just a column of 200 or so numbers? Or does it have the variable name also? Is the issue that you want to match a list of 200 or so values with a list of 200 or so variables? That can be done fairly easily.

@lasseledet Give me the values of the parameters and I'll try to find something.

You said that the root that you want is close to -1+I. You can use RootFinding:-Analytic with the range being a box centered at -1+I.

You could let k = x+I*y, then use DirectSearch:-SolveEquations on Re(DispersionEq) and Im(DispersionEq).

@lasseledet Do you have numeric values for Omega, Zeta, lambda, nu, rho, and gamma__o? Without numeric values, I think that it is hopeless. With numeric values, I think that it will be easy with fsolve or another root finder.

@Mac Dude My reading is that by "export" the OP means to write out the values so that they can be read by another program. For that, we need to know the format that the other program accepts.

In this post, Samir Khan does it by using a textplopt on each contour.

It is not clear to me what you mean by the minus sign in f^-2. Do you mean something having to do with an inverse function? From your subsequent code, it looks like you intended merely the second derivative. But why the minus sign?

What do you hope to achieve from a symbolic solution to this problem that you can't get from a numeric solution? Maybe we can show you how to get it from the numeric solution. The symbolic solution is unwieldy, and I doubt that it can be significantly improved.

@acer 

solve(x^2 - 2*(m+1)*x+m^2 - 2*m + m^2=0,{x},real,parametric=full);